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

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Introduction to trignometry

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

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.

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.

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 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.

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.

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.

Height and distances

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.

Introduction to trignometry

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

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.

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.

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 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.

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.

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.

Height and distances

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.

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.

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.

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.

Some applications on Trigonometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines angle of elevation and depression, and provides examples of using trigonometric ratios to calculate the height of a tower, pole, and kite string based on observed angles of elevation or depression. Sample problems are worked through showing the application of trigonometric functions like tangent and sine to find unknown lengths.

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

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.

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.

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

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient times and is used across many fields including astronomy, navigation, architecture, engineering, and digital imaging. Trigonometric functions relate ratios of sides of a right triangle to an angle of the triangle. These functions and their relationships are important tools that are applied in problems involving waves, forces, rotations, and more.

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.

Basic trigonometry

This document provides an overview of basic trigonometry. It defines trigonometry as the study of relationships involving lengths and angles of triangles, and notes that it emerged from applications of geometry to astronomy. The document explains the key parts of a right triangle, the trigonometric ratios of sine, cosine and tangent, and the SOHCAHTOA mnemonic. It also covers important angles, Pythagoras' theorem, other trigonometric ratios, the unit circle, and trigonometric functions and identities. Links are provided for additional online resources on trigonometry.

Introduction to trigonometry

This document provides an introduction to trigonometry. It defines trigonometry as dealing with relations of sides and angles of triangles. It discusses the history of trigonometry and defines the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent). It provides the ratios for some specific angles and identities relating the ratios. It describes applications of trigonometry in fields like astronomy, navigation, architecture, and more.

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.

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

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

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.

PPT on Trigonometric Functions. Class 11

Trigonometry deals with relationships between sides and angles of triangles. It originated in ancient Greece and was used to calculate sundials. Key concepts include trigonometric functions like sine, cosine and tangent that relate a triangle's angles to its sides. Trigonometric identities and angle formulae allow for the conversion between functions. It has wide applications in fields like astronomy, engineering and navigation.

Trigonometry

What is Trigonometry?
Basic Concepts that will give you a better idea of Trigonometry.
What can you do with Trigonometry...

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.

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.

Trignometry

Hello everyone...There are many teachers in the schools which gives students to make a powerpoint presentation on Maths topic...most of students get confused that what to make...so now no need to worry about...you can download it!
Thank You

นำเสนอตรีโกณมิติจริง

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been used for thousands of years in fields like astronomy, navigation, architecture, engineering, and more modern fields like digital imaging and computer graphics. Trigonometric functions define ratios between sides of a right triangle and are used to solve for unknown sides and angles. Common applications include calculating distances, heights, satellite positioning, and modeling waves and vibrations.

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.

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.

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.

Some applications on Trigonometry

This document discusses trigonometry and how it can be used to calculate heights and distances. It defines angle of elevation and depression, and provides examples of using trigonometric ratios to calculate the height of a tower, pole, and kite string based on observed angles of elevation or depression. Sample problems are worked through showing the application of trigonometric functions like tangent and sine to find unknown lengths.

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

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.

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.

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

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient times and is used across many fields including astronomy, navigation, architecture, engineering, and digital imaging. Trigonometric functions relate ratios of sides of a right triangle to an angle of the triangle. These functions and their relationships are important tools that are applied in problems involving waves, forces, rotations, and more.

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.

Basic trigonometry

This document provides an overview of basic trigonometry. It defines trigonometry as the study of relationships involving lengths and angles of triangles, and notes that it emerged from applications of geometry to astronomy. The document explains the key parts of a right triangle, the trigonometric ratios of sine, cosine and tangent, and the SOHCAHTOA mnemonic. It also covers important angles, Pythagoras' theorem, other trigonometric ratios, the unit circle, and trigonometric functions and identities. Links are provided for additional online resources on trigonometry.

Introduction to trigonometry

This document provides an introduction to trigonometry. It defines trigonometry as dealing with relations of sides and angles of triangles. It discusses the history of trigonometry and defines the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent). It provides the ratios for some specific angles and identities relating the ratios. It describes applications of trigonometry in fields like astronomy, navigation, architecture, and more.

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.

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

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

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.

PPT on Trigonometric Functions. Class 11

Trigonometry deals with relationships between sides and angles of triangles. It originated in ancient Greece and was used to calculate sundials. Key concepts include trigonometric functions like sine, cosine and tangent that relate a triangle's angles to its sides. Trigonometric identities and angle formulae allow for the conversion between functions. It has wide applications in fields like astronomy, engineering and navigation.

Trigonometry

What is Trigonometry?
Basic Concepts that will give you a better idea of Trigonometry.
What can you do with Trigonometry...

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.

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.

Maths ppt on some applications of trignometry

Maths ppt on some applications of trignometry

Application of trigonometry

Application of trigonometry

Some application of trignometry

Some application of trignometry

Some applications on Trigonometry

Some applications on Trigonometry

Ppt on trignometry by damini

Ppt on trignometry by damini

Trigonometry

Trigonometry

Trigonometry maths school ppt

Trigonometry maths school ppt

Mathematics ppt on trigonometry

Mathematics ppt on trigonometry

Trigonometry

Trigonometry

Heights & distances

Heights & distances

Basic trigonometry

Basic trigonometry

Introduction to trigonometry

Introduction to trigonometry

Applications of trignometry

Applications of trignometry

some applications of trigonometry 10th std.

some applications of trigonometry 10th std.

Introduction to trigonometry

Introduction to trigonometry

Trigonometry project

Trigonometry project

PPT on Trigonometric Functions. Class 11

PPT on Trigonometric Functions. Class 11

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Applications of trigonometry

Applications of trigonometry

Trignometry

Hello everyone...There are many teachers in the schools which gives students to make a powerpoint presentation on Maths topic...most of students get confused that what to make...so now no need to worry about...you can download it!
Thank You

นำเสนอตรีโกณมิติจริง

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been used for thousands of years in fields like astronomy, navigation, architecture, engineering, and more modern fields like digital imaging and computer graphics. Trigonometric functions define ratios between sides of a right triangle and are used to solve for unknown sides and angles. Common applications include calculating distances, heights, satellite positioning, and modeling waves and vibrations.

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.

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.

Trigonometry ratios in right triangle

This document discusses right triangle trigonometry. It defines the six trigonometric functions as ratios of sides of a right triangle. The sides are the hypotenuse, adjacent side, and opposite side relative to an acute angle. It shows how to calculate trig functions for a given angle and how to find an unknown angle given two sides of a right triangle using inverse trig functions. Examples are provided to demonstrate solving for missing sides and angles of right triangles using trig ratios and the Pythagorean theorem.

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.

TRIGONOMETRY

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy in ancient Greece. The word trigonometry comes from Greek words meaning "three", "sides", and "measure". Trigonometry defines ratios between the sides and angles of right triangles, and establishes trigonometric identities that are true for all angle values. These identities relate trigonometric functions of complementary angles and derive important equations like the Pythagorean identity.

Planetrigonometr Yisbasedonthefactofs

The document discusses plane trigonometry and how it is based on similar figures having equal angles and proportional sides, focusing on using trigonometric functions like sine, cosine, and tangent to indirectly measure quantities like heights or distances that cannot be measured directly by using known measurements and angle relationships in right triangles. Examples are provided for how trigonometry can be used to calculate the height of a flagpole or lighthouse given a measured distance and angle of elevation.

5.4 Solving Right Triangles

The document discusses solving right triangles by using trigonometric ratios to find missing angles and sides given certain information like an angle measurement or side length. It also covers solving problems involving angles of elevation and depression by setting up trigonometric equations and solving for the unknown based on a sketch of the situation. Examples are provided to demonstrate these problem solving techniques step-by-step.

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.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like navigation, engineering, and astronomy. Trigonometry specifically studies right triangles, where one angle is 90 degrees. The Pythagorean theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent are used to calculate unknown sides and angles based on known values. Trigonometry has many applications in areas involving waves, geometry, and modeling real-world phenomena.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like astronomy, engineering, and digital imaging. Trigonometry specifically studies right triangles and defines trigonometric functions like sine, cosine, and tangent that relate a triangle's angles and sides. Key concepts include trigonometric ratios, the Pythagorean theorem, trigonometric identities, and applications to problems involving distance, direction, and waves.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been developed and used for over 4000 years, originating in ancient civilizations for purposes like calculating sundials. A key foundation is the right triangle, where one angle is 90 degrees. Pythagoras' theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent define relationships between sides and angles. Trigonometry has many applications, from astronomy and navigation to engineering, physics, and digital imaging.

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For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
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- 2. Trigonometry is the branch of mathematics that deals with triangles particularly right triangles. They are behind how sound and light move and are also involved in our perceptions of beauty and other facets on how our mind works. So trigonometry turns out to be the fundamental to pretty much everything!
- 3. A trigonometric function is a ratio of certain parts of a triangle. The names of these ratios are: The sine, cosine, tangent, cosecant, secant, cotangent. Let us look at this triangle… a c b ө A B C Given the assigned letters to the sides and angles, we can determine the following trigonometric functions. Sinθ= Cos θ= Tan θ= Side Opposite Hypotenuse Side Adjacent Hypotenuse Side Opposite Side Adjacent = = a c b c = a b
- 4. 1 1 1 1 1 45 2 45 2 45 Sin Cos Tan 3 1 3 30 2 30 1 2 30 Sin Cos Tan 3 3 1 1 60 2 60 2 60 Sin Cos Tan 0 0 1 0 1 0 1 1 0 0 1 0 Sin Cos Tan Sin Cos 1 0 1 Tan n . d 0 90 1 90 1 1 90
- 5. One of the most ancient subjects studied by scholars all over the world, astronomers have used trigonometry to calculate the distance from the earth to the planets and stars. Its also used in geography and in navigation. The knowledge of trigonometry is used to construct maps, determine the position of an island in relation to longitudes and latitudes. Trigonometry is used in almost every sphere of life around you. Angle of depression Angle of elevation
- 6. Angle of Elevation: In the picture below, an observer is standing at the top of a building is looking straight ahead (horizontal line). The observer must raise his eyes to see the airplane (slanting line). This is known as the angle of elevation. Angle of elevation Horizontal
- 7. Angle of Depression: The angle below horizontal that an observer must look to see an object that is lower than the observer. Horizontal Angle of depression Object
- 8. The angle of elevation of the top of a pole measures 45° from a point on the ground 18 ft. away from its base. Find the height of the flagpole. Solution Let’s first visualize the situation Let ‘x’ be the height of the flagpole. From triangle ABC, tan 45 ° =x/18 x = 18 × tan 45° = 18 × 1=18ft So, the flagpole is 18 ft. high. 45 °
- 9. A tower stands on the ground. The angle of elevation from a point on the ground which is 30 metres away from the foot Of the tower is 30⁰. Find the height of the tower. (Take √3 = 1.732) Let AB be the tower h metre high. Let C be a point on the ground which is 30 m away from point B, the foot of the tower. 30⁰ So BC = 30 m Then ACB = 30⁰ Now we have to find AB i.e. height ‘h’ of the tower . 30 m h A B C Solution .
- 10. Now we shall find the trigonometric ratio combining AB and BC . AB B tan 30⁰ 1 √3 h 30 h 30 √3 30 x √3 √3 x √3 30 x √3 3 10√3 m 10 x 1.732 m 17.32 m Hence, height of the tower = 17.32 m 30⁰ 30 m h A B C
- 11. An airplane is flying at a height of 2 miles above the level ground. The angle of depression from the plane to the foot of a tree is 30°. Find the distance that the air plane must fly to be directly above the tree. 30 ° 30 ° Step 1: Let ‘x’ be the distance the airplane must fly to be directly above the tree. Step 2: The level ground and the horizontal are parallel, so the alternate interior angles are equal in measure. Step 3: In triangle ABC, tan 30=AB/x. Step 4: x = 2 / tan 30 Step 5: x = (2*31/2) Step 6: x = 3.464 So, the airplane must fly about 3.464 miles to be directly above the tree. D