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Trigonometry is used to calculate unknown heights, distances, and angles using relationships between sides and angles of triangles. It was developed by ancient Greek mathematicians like Thales and Hipparchus to solve problems in astronomy and geography. Some key applications include using trigonometric ratios like tangent and cotangent along with known distances and angles of elevation/depression to determine the height of objects like towers, buildings, and mountains when direct measurement is not possible. The document provides historical context and examples to illustrate how trigonometric concepts have been applied to problems involving finding heights, distances, and other unknown measurements through the use of triangles and their properties.

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Some application of trignometry

Trigonometry deals with right triangles and angles, and is used in fields like sound, light, and perceptions of beauty. The document defines common trigonometric terms like angle of elevation, angle of depression, sine, cosine, and tangent. It provides examples of using trigonometric functions to solve problems like finding the height of a tower or flagpole given angle of elevation measurements. Several practice problems on trigonometry are also presented and solved.

Maths ppt on some applications of trignometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Maths project --some applications of trignometry--class 10

Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.

Real World Application of Trigonometry

Trigonometry is a branch of mathematics that studies triangles and their relationships. The document discusses how trigonometry is used in the fields of architecture, astronomy, and geology. In architecture, trigonometry is used to calculate angles to ensure structural stability and safety. Astronomers use trigonometry and concepts like parallax to calculate distances between stars. Geologists use trigonometry to estimate true dip angles of bedding to determine slope stability important for building foundations.

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Heights & distances

Trigonometry deals with calculating distances and heights using mathematical techniques. It originated in ancient Greece and Egypt for purposes like astronomy and geography. Hipparchus is considered one of the founders of trigonometry for developing quantitative models of celestial motions. Trigonometry is now widely used in fields like calculus, physics, engineering, and more. It allows calculating inaccessible lengths like heights and widths using angles of elevation, depression, and trigonometric functions like sine, cosine, and tangent.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Some application of trignometry

Trigonometry deals with right triangles and angles, and is used in fields like sound, light, and perceptions of beauty. The document defines common trigonometric terms like angle of elevation, angle of depression, sine, cosine, and tangent. It provides examples of using trigonometric functions to solve problems like finding the height of a tower or flagpole given angle of elevation measurements. Several practice problems on trigonometry are also presented and solved.

Maths ppt on some applications of trignometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Maths project --some applications of trignometry--class 10

Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.

Real World Application of Trigonometry

Trigonometry is a branch of mathematics that studies triangles and their relationships. The document discusses how trigonometry is used in the fields of architecture, astronomy, and geology. In architecture, trigonometry is used to calculate angles to ensure structural stability and safety. Astronomers use trigonometry and concepts like parallax to calculate distances between stars. Geologists use trigonometry to estimate true dip angles of bedding to determine slope stability important for building foundations.

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Heights & distances

Trigonometry deals with calculating distances and heights using mathematical techniques. It originated in ancient Greece and Egypt for purposes like astronomy and geography. Hipparchus is considered one of the founders of trigonometry for developing quantitative models of celestial motions. Trigonometry is now widely used in fields like calculus, physics, engineering, and more. It allows calculating inaccessible lengths like heights and widths using angles of elevation, depression, and trigonometric functions like sine, cosine, and tangent.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Trigonometry, Applications of Trigonometry CBSE Class X Project

A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student

some applications of trigonometry 10th std.

Trigonometry is mainly used in astronomy to measure distances of various stars. It is also used in measurement of heights of mountains, buildings, monument, etc.The knowledge of trigonometry also helps us to construct maps, determine the position of an island in relation to latitudes, longitudes

Some applications of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, including the angles of elevation and depression. It provides examples of using trigonometry to find the height of a tower from the angle of elevation measured 30 meters away (30 meters high), and the height of a pole from the angle made by a rope tied to its top (10 meters high). It also explains calculating the length of a kite string from the angle of elevation.

Applications of trignometry

Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.

Application of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, such as of trees, towers, water tanks, and distance from a ship to a lighthouse. It provides examples of using trigonometry to calculate the height of a tower given the angle of elevation and distance from its base, and the height of a pole given the angle made by the rope tied to its top and the ground.

trigonometry and application

Trigonometry is derived from Greek words meaning "three angles" and "measure". It deals with relationships between sides and angles of triangles, especially right triangles. The document discusses the history of trigonometry dating back to ancient Egypt and Babylon, and how it advanced through the works of Greek astronomer Hipparchus and Ptolemy. It also discusses the six trigonometric ratios and their formulas, various trigonometric identities, and applications of trigonometry in fields like architecture, engineering, astronomy, music, optics, and more.

Mathematics ppt on trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.

Trigonometry project

Trigonometry is the branch of mathematics dealing with triangles and trigonometric functions of angles. It is derived from Greek words meaning "three angles" and "measure". Trigonometry specifically studies relationships between sides and angles of triangles, and calculations based on trigonometric functions like sine, cosine, and tangent. Trigonometry has many applications in fields like astronomy, navigation, architecture, engineering, and more.

Maths project some applications of trignometry- class10 ppt

The document provides an introduction to trigonometry and its applications. It discusses how trigonometry deals with triangles, particularly right triangles, and involves angles and relationships between sides. The document then gives examples of using basic trigonometric ratios like sine, cosine, and tangent to solve problems involving unknown heights or distances. It provides historical context on how trigonometry was used in ancient times for applications like determining the height of structures. Overall, the document outlines fundamental trigonometric concepts and illustrates how trigonometry can be applied to calculate unknown measurements.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Introduction of trigonometry

Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers

Math project some applications of trigonometry

Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.

Trigonometry Presentation For Class 10 Students

Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Trigonometry maths school ppt

Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.

PPT ON TRIANGLES FOR CLASS X

1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.

Triangles and its properties

The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.

Class IX Heron's Formula

The document discusses Heron's formula for calculating the area of a triangle. Heron's formula uses the lengths of the three sides of a triangle to calculate its area, rather than requiring the base and height. The formula is defined as the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (half the perimeter) and a, b, c are the three side lengths. The formula is useful when it is difficult to measure the base and height of a triangle directly. An example problem demonstrates calculating the area of a triangle with side lengths 3cm, 4cm, and 5cm using Heron's formula.

Height & distance

This document contains 6 practice problems related to height and distance formulas involving angles of elevation. For each problem, the relevant information is provided, such as measurements of angles, distances, heights, etc. The formula used is stated and calculations are shown to arrive at the answer. All problems can be solved using basic trigonometric concepts of tangent, cosine and cotangent functions applied to triangles formed by heights, distances and angles of elevation.

Inverse trigonometric functions xii[1]

1) The document defines and discusses the domains and ranges of inverse trigonometric functions such as sin-1x, cos-1x, and tan-1x.
2) The inverse functions are defined based on reflecting portions of the original trigonometric functions over the line y=x.
3) The domains and ranges of the inverse functions are restricted to ensure each inverse function is a single-valued function.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Trigonometry, Applications of Trigonometry CBSE Class X Project

A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student

some applications of trigonometry 10th std.

Trigonometry is mainly used in astronomy to measure distances of various stars. It is also used in measurement of heights of mountains, buildings, monument, etc.The knowledge of trigonometry also helps us to construct maps, determine the position of an island in relation to latitudes, longitudes

Some applications of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, including the angles of elevation and depression. It provides examples of using trigonometry to find the height of a tower from the angle of elevation measured 30 meters away (30 meters high), and the height of a pole from the angle made by a rope tied to its top (10 meters high). It also explains calculating the length of a kite string from the angle of elevation.

Applications of trignometry

Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.

Application of trigonometry

Trigonometry studies triangles and relationships between sides and angles. This document discusses using trigonometric ratios to calculate heights and distances, such as of trees, towers, water tanks, and distance from a ship to a lighthouse. It provides examples of using trigonometry to calculate the height of a tower given the angle of elevation and distance from its base, and the height of a pole given the angle made by the rope tied to its top and the ground.

trigonometry and application

Trigonometry is derived from Greek words meaning "three angles" and "measure". It deals with relationships between sides and angles of triangles, especially right triangles. The document discusses the history of trigonometry dating back to ancient Egypt and Babylon, and how it advanced through the works of Greek astronomer Hipparchus and Ptolemy. It also discusses the six trigonometric ratios and their formulas, various trigonometric identities, and applications of trigonometry in fields like architecture, engineering, astronomy, music, optics, and more.

Mathematics ppt on trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.

Trigonometry project

Trigonometry is the branch of mathematics dealing with triangles and trigonometric functions of angles. It is derived from Greek words meaning "three angles" and "measure". Trigonometry specifically studies relationships between sides and angles of triangles, and calculations based on trigonometric functions like sine, cosine, and tangent. Trigonometry has many applications in fields like astronomy, navigation, architecture, engineering, and more.

Maths project some applications of trignometry- class10 ppt

The document provides an introduction to trigonometry and its applications. It discusses how trigonometry deals with triangles, particularly right triangles, and involves angles and relationships between sides. The document then gives examples of using basic trigonometric ratios like sine, cosine, and tangent to solve problems involving unknown heights or distances. It provides historical context on how trigonometry was used in ancient times for applications like determining the height of structures. Overall, the document outlines fundamental trigonometric concepts and illustrates how trigonometry can be applied to calculate unknown measurements.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Introduction of trigonometry

Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers

Math project some applications of trigonometry

Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.

Trigonometry Presentation For Class 10 Students

Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Trigonometry maths school ppt

Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.

PPT ON TRIANGLES FOR CLASS X

1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.

Triangles and its properties

The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.

Class IX Heron's Formula

The document discusses Heron's formula for calculating the area of a triangle. Heron's formula uses the lengths of the three sides of a triangle to calculate its area, rather than requiring the base and height. The formula is defined as the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (half the perimeter) and a, b, c are the three side lengths. The formula is useful when it is difficult to measure the base and height of a triangle directly. An example problem demonstrates calculating the area of a triangle with side lengths 3cm, 4cm, and 5cm using Heron's formula.

Ppt on trignometry by damini

Ppt on trignometry by damini

Trigonometry, Applications of Trigonometry CBSE Class X Project

Trigonometry, Applications of Trigonometry CBSE Class X Project

some applications of trigonometry 10th std.

some applications of trigonometry 10th std.

Some applications of trigonometry

Some applications of trigonometry

Applications of trignometry

Applications of trignometry

Application of trigonometry

Application of trigonometry

trigonometry and application

trigonometry and application

Mathematics ppt on trigonometry

Mathematics ppt on trigonometry

Trigonometry project

Trigonometry project

Maths project some applications of trignometry- class10 ppt

Maths project some applications of trignometry- class10 ppt

Trigonometry

Trigonometry

Trigonometry presentation

Trigonometry presentation

Introduction of trigonometry

Introduction of trigonometry

Math project some applications of trigonometry

Math project some applications of trigonometry

Trigonometry Presentation For Class 10 Students

Trigonometry Presentation For Class 10 Students

Introduction to trignometry

Introduction to trignometry

Trigonometry maths school ppt

Trigonometry maths school ppt

PPT ON TRIANGLES FOR CLASS X

PPT ON TRIANGLES FOR CLASS X

Triangles and its properties

Triangles and its properties

Class IX Heron's Formula

Class IX Heron's Formula

Height & distance

This document contains 6 practice problems related to height and distance formulas involving angles of elevation. For each problem, the relevant information is provided, such as measurements of angles, distances, heights, etc. The formula used is stated and calculations are shown to arrive at the answer. All problems can be solved using basic trigonometric concepts of tangent, cosine and cotangent functions applied to triangles formed by heights, distances and angles of elevation.

Inverse trigonometric functions xii[1]

1) The document defines and discusses the domains and ranges of inverse trigonometric functions such as sin-1x, cos-1x, and tan-1x.
2) The inverse functions are defined based on reflecting portions of the original trigonometric functions over the line y=x.
3) The domains and ranges of the inverse functions are restricted to ensure each inverse function is a single-valued function.

Maths A - Chapter 5

This document provides information about Pythagoras' theorem and how it can be used to solve problems involving right triangles. It begins with a brief history of Pythagoras and the times he lived in. It then explains Pythagoras' theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Examples are provided to demonstrate how to use the theorem to calculate unknown sides of right triangles. The document also notes that rearranging the theorem allows calculating the lengths of the shorter sides given the hypotenuse.

right triangles Application

This document contains multiple word problems involving right triangles and trigonometric functions like sine, cosine, and tangent. It provides the problems, drawings of the relevant right triangles, and the step-by-step workings to arrive at the solutions. The problems cover a range of real-world scenarios involving angles of elevation/depression, shadows, ladders, towers, and more.

Nationalist movement in indo china

The document summarizes the history of French colonization in Vietnam from 1858 to 1975 in several paragraphs. Some key points:
1. France established control over Vietnam in the late 1800s and formed French Indochina in 1887, ruling the region as a colony.
2. Vietnamese resistance grew due to suffering under French rule, leading to nationalist movements.
3. After World War 2, Ho Chi Minh declared independence for Vietnam but France tried to regain control, leading to the First Indochina War.
4. The French were defeated in 1954 at the Battle of Dien Bien Phu, after which Vietnam was divided pending elections that never occurred. This led to war between North and South

Aptitude Age Problems

The document contains 10 problems related to ages and ratios of ages. It provides the problems, solutions, and explanations. The problems involve calculating ages given information about the ratios of ages between people over time. For each problem, the correct answer is identified from the multiple choice options provided.

Internship report on retail banking activities of city bank ltd by lectureshe...

Internship report on retail banking activities of city bank ltd by lectureshe...International Islamic University Chittagong, Batch 28 A9

The document provides an overview of City Bank Ltd., including its background, vision, mission, strategies, organizational structure, functions, and departments. Some key points:
- City Bank Ltd. is one of the oldest private commercial banks in Bangladesh, operating since 1983 with 86 branches across the country.
- Its vision is to be the leading bank in the country with best practices and highest social commitment.
- It has four main business divisions: corporate banking, retail banking, SME banking, and treasury.
- The report discusses the bank's location-based and business-level strategies to focus on strengthening existing branches and retail/SME banking.Projekt Matemaik - Matjet e Paarritshme

Matjete e paarrtishme , problem

MATEMATIKE AVANC: "Matja e objekteve te paarritshme ndermjet funksioneve trig...

PROJEKT MATEMATIKE AVANC
KLASA XI-7
SHKOLLA MYSLYM KETA
VITI SHKOLLOR: 2014-2015
PRANOI: DREJTORI DASHNOR HOXHA

Angular measurements

This document discusses various instruments used to measure angles:
- Protractors, bevel protractors, vernier bevel protractors, and optical bevel protractors are used to measure angles between two faces. Vernier bevel protractors provide more precise readings through a vernier scale.
- Sine bars and sine centers are used with slip gauges to measure angles through trigonometric functions. Sine bars become inaccurate for angles over 45 degrees.
- Angle gauges precisely measure angles through calibrated blocks that can be added or subtracted.
- Spirit levels and clinometers measure angles of incline relative to horizontal, with clinometers providing a scale to measure the exact

Cesar Chavez

Cesar Chavez was a Mexican American civil rights and labor leader who fought for better working conditions for migrant farm workers. He organized the United Farm Workers union and led a nationwide grape boycott and strikes that lasted for years. Though the workers faced hardships and oppression, their efforts improved wages and rights for migrant laborers. Chavez became a prominent advocate for social justice and remained dedicated to the farm worker cause until his death in 1993, where over 40,000 people mourned the loss of his leadership.

MEASURING LENGTH (teach)

1. The document discusses the history and development of systems for measuring length and distance, from early rulers based on body parts to the modern metric system.
2. It describes how the metric system was developed using the distance from the Earth's equator to the North Pole, divided into 10 million equal parts called meters.
3. The document provides examples of measuring various lengths in millimeters and centimeters using a metric ruler, and explains how the metric units of meters, centimeters and millimeters are used to measure different distances.

Distance and displacement

The document discusses the differences between distance and displacement. Distance refers to the total length of the path traveled, while displacement refers to the straight line distance between the starting and ending points. Displacement can be zero if the ending point is the same as the starting point, while distance traveled would still be greater than zero in this case. Both distance and displacement would be zero if an object returns to its original starting point.

Nationalist Movement in Indo - china (CBSE X)

The document discusses the nationalist movement in Indo-China, which consists of Vietnam, Laos, and Cambodia. It describes how Vietnam was under Chinese influence for many years but was later colonized by France in the late 1800s. The French developed infrastructure projects but faced resistance from Vietnamese nationalists who advocated for independence. The movement was inspired by leaders like Ho Chi Minh and was aided by women who played important roles in the struggle against foreign domination. The US eventually became involved in backing South Vietnam, leading to prolonged war and suffering until a peace agreement was reached in 1974.

tacheometry surveying

Tacheometry is a surveying method that uses optical instruments like a theodolite fitted with a stadia diaphragm to measure horizontal and vertical distances between points. It works on the principle that the ratio of distance from the instrument to the base of an isosceles triangle and the length of the base is constant. Distances are calculated using stadia intercept readings and multiplying constants based on the focal length of the instrument's objective lens. Tacheometry offers faster measurement compared to traditional chaining and is useful for surveys in difficult terrain like rivers, valleys, or undulating ground where conventional surveying would be inaccurate or slow.

Congruence of triangles

This document discusses congruence of triangles, which is when two triangles have the same shape and size, meaning one triangle can be repositioned to coincide precisely with the other. It provides examples of congruent and non-congruent triangles based on equal angles and side lengths. The key properties for congruence of triangles are that they must have equal measures of angles and equal lengths of sides.

Symmetry In Math

There are several basic types of symmetry including line symmetry, rotational symmetry, translational symmetry, reflective symmetry, and glide reflective symmetry. Symmetry can be seen in art, nature, mathematics and other areas. The document discusses these types of symmetries and provides examples like kaleidoscopes, wheels, and shapes to illustrate symmetrical concepts. Exercises are suggested to help understand symmetry further such as folding paper or moving shapes on a plane.

Tacheometry ppt

This document provides information about tacheometry, which is a method of surveying that determines horizontal and vertical distances from instrumental observations. It discusses how tacheometry can be used when obstacles make traditional surveying difficult. The key aspects covered include:
- Defining tacheometry and the measurements it provides
- When tacheometry is advantageous over other surveying methods
- The instruments used, including tacheometers and levelling rods
- How horizontal and vertical distances are calculated using constants
- The different types of tacheometer diaphragms and telescopes
- The fixed hair method for taking readings

Tacheometric survey

1. The document presents information from a slideshow on tacheometric surveying. It discusses various methods of tacheometric surveying including fixed hair, movable hair, tangential, and subtense bar methods.
2. Formulas are provided for calculating horizontal distance, vertical distance, and elevation of points using these different tacheometric surveying methods under various sighting conditions such as inclined or depressed lines of sight.
3. The document also discusses tacheometric constants, anallatic lenses, and procedures for conducting field work in a tacheometric survey including selecting instrument stations, taking observations of vertical angles and staff readings, and shifting to subsequent stations.

Height & distance

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Inverse trigonometric functions xii[1]

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Applications of trigonometry

Trigonometry was invented by ancient Greeks to calculate distances and angles in astronomy. It relates the angles and lengths of triangles, allowing unknown values to be determined if one angle and one length are known. Some early applications included creating trigonometric tables for astronomical computations and using triangulation to measure heights and distances. Modern uses include navigation, surveying, engineering, acoustics, and technologies like GPS which rely on trigonometric calculations.

Ebook on Elementary Trigonometry by Debdita Pan

Trigonometry is a branch of Mathematics that deals with the distances or heights of objects which can be found using some mathematical techniques. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three) , ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, trigonometry is used in physics, engineering, and chemistry. Within mathematics, trigonometry is used primarily in calculus (which is perhaps its greatest application), linear algebra, and statistics. Since these fields are used throughout the natural and social sciences, trigonometry is a very useful subject to know

Ebook on Elementary Trigonometry By Debdita Pan

A Short Introduction to Trigonometry. Trigonometry blends a bit of geometry with a lot of common sense. It lets you solve problems that is of common life and experience.

Pythagoras thms..

The document discusses the history and development of the Pythagorean theorem. It explains that Pythagoras founded a philosophical school in Croton, Italy, where he and his followers studied mathematics and believed that numbers were the ultimate reality. The document then provides several proofs of the Pythagorean theorem, including using similar triangles, adding the areas of shapes, and the converse theorem. It also discusses Pythagoras' contributions to music and other areas of mathematics.

Trigonometry class10.pptx

This document provides an overview of trigonometry. It defines trigonometry as dealing with relationships between sides and angles of triangles, particularly right triangles. The origins of trigonometry can be traced back 4000 years to ancient civilizations. Key concepts discussed include right triangles, the Pythagorean theorem, trigonometric ratios like sine, cosine and tangent, and applications of trigonometry in fields like construction, astronomy, and engineering. Examples are provided for using trigonometric functions to solve problems involving heights and distances.

Some Applications of Trigonometry

This document discusses trigonometry and its applications. It defines trigonometry as the measurement of triangles and angles, and notes its Greek roots. Some key applications are mentioned like surveying, navigation, physics and engineering. It defines angle of elevation and depression. It then provides an example problem to find the distance between two ships based on the observed angle of elevation of a lighthouse from each ship.

Mathematics-Inroduction to Trignometry Class 10 | Smart eTeach

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The document provides an overview of the history and development of trigonometry. It discusses how trigonometry originated in ancient Greece and Mesopotamia for applications in astronomy and was further developed by Greek mathematicians such as Hipparchus. Key concepts in trigonometry like trig functions, trig identities, and trig ratios are also explained.

applications of trignomerty

Trigonometry is a branch of mathematics that studies relationships between sides and angles of triangles. It emerged from Greek astronomy studies in the 3rd century BC. Classical Greek mathematicians proved theorems equivalent to modern trigonometric formulas, though presented geometrically rather than algebraically. Indian mathematicians in the 4th-5th century defined trig functions like sine and cosine. Trigonometry has many applications including triangulation used in astronomy, geography, and navigation. Examples are also given of using trig ratios to solve problems involving angles of elevation and depression to find distances.

Trigonometry Exploration

The document discusses trigonometry and provides definitions and examples of its uses. It defines trigonometry as the branch of mathematics dealing with relationships involving lengths and angles of triangles. It then gives examples of how trigonometry is used in fields like navigation, architecture, engineering, and game development. It also provides information on trigonometric functions like sine waves and their importance in fields like physics and signal processing.

Learning network activity 3

Trigonometry is a branch of mathematics that deals with relationships between the sides and angles of triangles, especially right triangles. It has many applications in fields like astronomy, navigation, engineering, and more. Some key uses of trigonometry include measuring inaccessible heights and distances by using trigonometric functions and properties of triangles formed by angles of elevation or depression. For example, trigonometry can be used to calculate the height of a building or tree by measuring the angle of elevation from a known distance away. It also has applications in measuring distances in astronomy, designing curved architectural structures, and calculating road grades. The document provides examples of various real-world applications of trigonometric concepts.

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope and the ground.

maths ppt on some applications of trignometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines trigonometric ratios and the angles of elevation and depression. It then provides examples of using trigonometry to calculate the height of a tower given the angle of elevation is 30 degrees and the distance from the observer is 30 meters. It also gives an example of calculating the height of a pole using the angle made by the rope attached to the top of the pole and the ground.

mathspptonsomeapplicationsoftrignometry-130627233940-phpapp02 (1).pptx

Trigonometry studies triangles and relationships between sides and angles. It uses trigonometric ratios to calculate heights and distances. There are two types of angles used - angle of elevation, which is the angle formed between the line of sight and horizontal when looking up, and angle of depression, which is the angle formed when looking down. Some example problems calculate heights and distances using trigonometric ratios and the given angles of elevation or depression.

Trignometry

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G4 measuring by trigonometry

1) A group of boys used trigonometry and angle measuring systems (AMS) to measure the height of a monument in a plaza.
2) They took angle measurements from two positions and measured the distance between the positions.
3) They then used trigonometric equations involving tangents, angles, and distances to calculate the height of the monument, which they determined to be 18.48 meters.
4) They acknowledged some potential errors in their angle measurements but concluded that trigonometry is a useful method for calculating heights and distances.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient civilizations over 4000 years ago and is used in many fields today including architecture, astronomy, engineering, and more. Trigonometric functions relate ratios of sides in a right triangle to the angles of the triangle. These functions and their relationships are important tools that allow calculations and problem solving across various domains.

Misbah_Fazal.pptx

1) The document describes an experiment to determine the radius of gyration of a compound pendulum by measuring its period of oscillation when suspended at different distances along its length.
2) Key steps include suspending the bar pendulum at different holes along its length and measuring the period of oscillation. This allows plotting period against suspension distance to determine the radius of gyration.
3) Analysis involves comparing the compound pendulum to an equivalent simple pendulum with the same period to calculate the radius of gyration and acceleration due to gravity.

CdEo5njkDLFm6Rno13.pptx

This document provides solutions to 16 questions about applications of trigonometry involving angles of elevation and depression. The questions calculate heights and distances using trigonometric ratios in right triangles formed by towers, poles, buildings, and other objects viewed from different points. The solutions demonstrate setting up and solving right triangle trig problems systematically to find the requested unknown values in each scenario.

Applications of trigonometry

Applications of trigonometry

Ebook on Elementary Trigonometry by Debdita Pan

Ebook on Elementary Trigonometry by Debdita Pan

Ebook on Elementary Trigonometry By Debdita Pan

Ebook on Elementary Trigonometry By Debdita Pan

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Trigonometry class10.pptx

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Mathematics-Inroduction to Trignometry Class 10 | Smart eTeach

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Hari love sachin

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applications of trignomerty

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Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

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maths ppt on some applications of trignometry

maths ppt on some applications of trignometry

mathspptonsomeapplicationsoftrignometry-130627233940-phpapp02 (1).pptx

mathspptonsomeapplicationsoftrignometry-130627233940-phpapp02 (1).pptx

Trignometry

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G4 measuring by trigonometry

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CdEo5njkDLFm6Rno13.pptx

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Structure of atom

Atoms are made up of tiny particles called protons, neutrons, and electrons. Protons and neutrons are located in the center of the atom in the nucleus, while electrons orbit around the nucleus. Over time, scientists developed models of the atom, starting with plum pudding model where electrons were embedded in a positive sphere, then Rutherford's model with a small dense nucleus at the center, and Bohr's model where electrons orbit in fixed shells around the nucleus. The number of protons determines the element, while the number of neutrons varies between isotopes of that element.

Green house effect

1) Greenhouse gases like carbon dioxide and methane trap heat in the atmosphere, causing Earth's surface temperature to be warmer than it would be otherwise.
2) The primary greenhouse gases are water vapor, carbon dioxide, methane, and nitrous oxide. Increased levels of carbon dioxide and methane from human activities are enhancing the greenhouse effect and leading to climate change.
3) If greenhouse gas levels continue to rise, the climate could experience a runaway greenhouse effect like on Venus, with surface temperatures too hot to sustain life. Immediate action is needed to reduce greenhouse gas emissions and transition to renewable energy sources.

Deforestation

Deforestation is disturbing animal habitats and endangering species as humans cut down many trees to build homes and for farming, polluting the air and leaving animals without homes, which can cause them to die from starvation or accidents. Photos show areas that were once forests being wiped away due to deforestation for development and agriculture. Conservation is needed to preserve forests, trees, clean air, and wildlife.

Solar energy

The document discusses various methods for harnessing solar energy, including passive and active solar heating systems for water and living spaces, as well as solar thermal and photovoltaic electricity generation. It describes technologies like power towers, parabolic dishes and troughs, and solar panels. While solar energy has benefits like being renewable and pollution-free, its intermittent nature and higher costs compared to fossil fuels have posed challenges to widespread adoption.

Light presentation

Light travels very fast in straight lines. We see objects because they reflect light into our eyes, forming shadows where light is blocked. Reflection follows the law that the angle of incidence equals the angle of reflection. Sound travels slower than light and we hear things when they vibrate at different frequencies and amplitudes. The ear contains structures like the eardrum, bones and cochlea that help detect and process sound vibrations.

Linear equation in 2 variables

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Structure of atom

Structure of atom

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- 2. Heights and Distances ? What you’re going to do ? next? 45o
- 3. In this situation , the distance or the heights can be founded by using mathematical techniques, which comes under a branch of ‘trigonometry’. The word ‘ trigonometry’ is derived from the Greek word ‘tri’ meaning three , ‘gon’ meaning sides and ‘metron’ meaning measures. Trigonometry is concerned with the relationship between the angles and sides of triangles. An understanding of these relationships enables unknown angles and sides to be calculated without recourse to direct measurement. Applications include finding heights/distances of objects.
- 6. Trigonometry An early application of trigonometry was made by Thales on a visit to Egypt. He was surprised that no one could tell him the height of the 2000 year old Cheops pyramid. He used his Thales of Miletus knowledge of the relationship between the heights of objects 640 – 546 B.C. The first Greek and the length of their shadows to calculate the height for Mathematician. He them. (This will later become the Tangent ratio.) Can you see what predicted the Solar Eclipse of 585 BC. this relationship is, based on the drawings below? h 480 ft 720 ft Similar Similar 6 ft Triangles Triangles 9 ft Sun’s rays casting shadows mid-afternoon Sun’s rays casting shadows late afternoon Thales may not have used similar triangles directly to solve the problem but h he knew that6the ratio of the 6x 720 horizontal sides of each triangle was vertical to h 480 ft sun. Can you use the constant and unchanging for different heights of the (Egyptian feet of course) 720 9 9 measurements shown above to find the height of Cheops?
- 7. Later, during the Golden Age of Athens (5 BC.), the philosophers and mathematicians were not particularly interested in the practical side of mathematics so trigonometry was not further developed. It was another 250 years or so, when the centre of learning had switched to Alexandria (current day Egypt) that the ideas behind trigonometry were more fully explored. The astronomer and mathematician, Hipparchus was the first person to construct tables of trigonometric ratios. Amongst his many notable achievements was his determination of the distance to the moon with an error of only 5%. He used the diameter of the Earth (previously calculated by Eratosthenes) together with angular measurements that had been taken during the total solar eclipse of March 190 BC. Eratosthenes Hipparchus of Rhodes 275 – 194 BC 190-120 BC
- 8. Early Applications of Trigonometry Finding the height of a mountain/hill. h 25o 20o x d Constructing sundials to Finding the distance to estimate the time from the moon. the sun’s shadow.
- 9. Historically trigonometry was developed for work in Astronomy and Geography. Today it is used extensively in mathematics and many other areas of the sciences. •Surveying •Navigation •Physics •Engineering
- 10. In this figure, the line AC drawn from the eye of the C student to the top of the tower is called the line of sight. The person is looking at the top of the tower. The angle BAC, so formed by Tower line of sight with horizontal is called angle of elevation. Angle of elevation A 45o Horizontal level B
- 11. A Horizontal level 45o Angle of depression Mountain Object C B
- 12. Method of finding the heights or the distances C Tower Angle of elevation A 45o Horizontal level B Let us refer to figure of tower again. If you want to find the height of the tower i.e. BC without actually measuring it, what information do you need ?
- 13. We would need to know the following: i. The distance AB which is the distance between tower and the person . ii. The angle of elevation angle BAC . Assuming that the above two conditions are given then how can we determine the height of the height of the tower ? In ∆ABC, the side BC is the opposite side in relation to the known angle A. Now, which of the trigonometric ratios can we use ? Which one of them has the two values that we have and the one we need to determine ? Our search narrows down to using either tan A or cot A, as these ratios involve AB and BC. Therefore, tan A = BC/AB or cot A = AB/BC, which on solving would give us BC i.e., the height of the tower.
- 14. Some Applications of trigonometry based on finding heights and distance
- 15. Here we have to find the height of the school. Here BC = 28.5 m and AC i.e., the height of the school = tan 45 = AC/BC i.e., 1 = AC/28.5 Therefore , AC = 28.5m So the height of the school is 28.5 m. A B 45o C 28.5m
- 16. Here we have to find the length of the ladder in the below figure and also how far is the foot of the ladder from the house ? (here take √3 = 1.73m) Now, can you think trigonometric ratios should we consider ? It should be sin 60 So, BC/AB = sin 60 or 3.7/AB = √3/2 B Therefore BC = 3.7 x 2/√3 Hence length of the ladder is 4.28m Now BC/AC = cot 60 = 1/√3 3.7m i.e., AC = 3.7/√3 = 2.14m (approx) 60o Therefore the foot of the ladder from the house is 2.14m. A C
- 17. Here we need to find the height of the lighthouse above the mountain . Given that AB = 10 m. (here take √3 =1.732). D 10 m B 30o 45o A P
- 18. Since we know the height of the mountain is AB so we consider the right ∆PAB. We have tan 30 = AB/AP i.e., 1/√3 = 10/AP therefore AP = 10√3m so the distance of the building = 10√3m = 17.32m Let us suppose DB = (10+x)m now in right ∆PAD tan 45 = AD/AP = 10+x/10√3 therefore 1 = 10+x/10√3 i.e., x = 10(√3-1) =7.32. So, the length of the flagstaff is 7.32m
- 19. Summary The line of sight is the line drawn from the eye of the observer to the point in the object viewed by the observer. The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object. The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level , i.e., the case when we lower our the head to look at the object. The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.
- 20. Thank you