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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.

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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.

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

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.

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.

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

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.

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.

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.

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.

Triangles

Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.

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

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has many applications in fields like architecture, astronomy, engineering, and more. The document provides background on trigonometry, defines trigonometric functions and ratios, discusses right triangles, and gives several examples of how trigonometry is used in areas like navigation, construction, and digital imaging.

Introduction To Trigonometry

This document provides an introduction to trigonometric ratios and identities. It defines the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) for an acute angle in a right triangle. It gives the specific trigonometric ratios for angles of 0°, 45°, 30°, 60°, and 90°. It also establishes the identities relating trigonometric ratios of complementary angles and the Pythagorean identities relating sine, cosine, tangent, cotangent, secant, and cosecant. Examples are provided to demonstrate how to use trigonometric identities to determine ratios when one ratio is known.

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.

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.

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.

Triangle Class-9th

This document discusses triangles and congruence. It defines a triangle as a closed figure with three intersecting lines and as having three sides, three angles, and three vertices. It then explains the meaning of congruence as equal in all respects and introduces three rules for determining if triangles are congruent: the Side-Angle-Side rule, the Angle-Side-Angle rule, and the Angle-Angle-Side rule. The document concludes with assigning homework questions involving congruent triangles.

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

Trigonometry

Trigonometry

some applications of trigonometry 10th std.

some applications of trigonometry 10th std.

Basic trigonometry

Basic trigonometry

Ppt on trignometry by damini

Ppt on trignometry by damini

Height and distances

Height and distances

Introduction to trignometry

Introduction to trignometry

Trigonometry

Trigonometry

Introduction to trigonometry

Introduction to trigonometry

Trigonometry

Trigonometry

Trigonometry maths school ppt

Trigonometry maths school ppt

Triangles

Triangles

Math project some applications of trigonometry

Math project some applications of trigonometry

Trigonometry

Trigonometry

Introduction To Trigonometry

Introduction To Trigonometry

Trigonometry ratios in right triangle

Trigonometry ratios in right triangle

trigonometry and application

trigonometry and application

Mathematics ppt on trigonometry

Mathematics ppt on trigonometry

Applications of trignometry

Applications of trignometry

Triangle Class-9th

Triangle Class-9th

Introduction of trigonometry

Introduction of trigonometry

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.

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

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-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.

Trignometry

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Angle of Elevation and Angle depression.pptx

The document defines and provides examples of calculating angles of elevation and depression. It explains that angle of elevation is formed when looking at an object higher than the observer, while angle of depression is formed when looking at an object lower than the observer. Examples are provided to demonstrate calculating unknown lengths using trigonometric functions like tangent, sine and cosine based on the angles of elevation or depression and known lengths.

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.

l4. elevation and depression

Here are the steps to solve this problem using trigonometry:
1. Draw a sketch of the situation showing the hot air balloon, observer, and relevant angles and distances.
2. Label the given information: The observer is 20 m from the base of the balloon and the angle of elevation is 35°.
3. Identify the trigonometric ratio to use based on the given and missing information. Since we are given an angle of elevation and the distance from the observer to the base of the balloon, we will use tangent.
4. Set up and solve the trigonometric equation:
Tan 35° = Opposite/Adjacent
Tan 35° = Height/20
Height = 20 * Tan

angle of depression and angle of elevation

angle of depression and angle of elevation
angle of depression and angle of elevation
angle of depression and angle of elevation

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.

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.

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

Math12 lesson 3

1) This document provides lesson objectives and examples for solving right triangles using trigonometric functions, the Pythagorean theorem, and angle relationships. It defines trigonometric ratios, angle of elevation/depression, bearing, and course.
2) Examples are provided to solve right triangles, find missing angles and sides, and solve real-world problems involving width of a stream, height of a flagpole, camera angle of depression, and height of a tower.
3) Additional examples solve problems involving slant distance to a sunken ship, plane bearings and courses between locations, and references are provided for further reading.

Trigonometry

The document discusses trigonometry and its uses in navigation, measuring heights and distances, and astronomical studies. It provides examples of trigonometric ratios like sine, cosine, and tangent for common angles. It then explains concepts like line of sight, angle of elevation and depression. It gives two word problems as examples - one calculating the height of a building given the observer's distance and angle of elevation, and another calculating the height a bird is flying given the angle of depression and distance to an object on the ground.

Rbse solutions for class 10 maths chapter 8 height and distance

The document contains 19 math word problems involving angles of elevation, depression, and shadows. It provides the questions, diagrams illustrating the problems, and step-by-step solutions. The problems cover topics like determining the height of towers, pillars, and hills using trigonometric ratios when given angles and distances.

Angles-of-Elevation-and-Depression.pptx

The document is about angles of elevation and depression. It provides examples to illustrate and differentiate between angles of elevation and depression. It gives practice problems identifying whether angles are of elevation or depression and solving word problems involving these angle types. Examples include finding distances given angles of elevation or depression from a plane or tower, or finding angles given distances and heights in situations involving the sun, kites, flagpoles, etc. Diagrams are provided with the problems to illustrate the geometry involved.

angle_of_elevation_depression cot2.pptx

This document provides information about angles of elevation and depression. It defines key terms like line of sight, angle of elevation, and angle of depression. It presents examples of how to classify angles as elevation or depression and solve problems involving right triangles using trigonometric ratios. The document also discusses applications of elevation and depression angles in fields like engineering and gives sample evaluation questions.

presentation_trigonometry.pptx

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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 (1).pptx

mathspptonsomeapplicationsoftrignometry-130627233940-phpapp02 (1).pptx

maths ppt on some applications of trignometry

maths ppt on some applications of trignometry

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

Mathspptonsomeapplicationsoftrignometry 130627233940-phpapp02

Trignometry

Trignometry

Angle of Elevation and Angle depression.pptx

Angle of Elevation and Angle depression.pptx

CdEo5njkDLFm6Rno13.pptx

CdEo5njkDLFm6Rno13.pptx

l4. elevation and depression

l4. elevation and depression

angle of depression and angle of elevation

angle of depression and angle of elevation

Trigonometry class10.pptx

Trigonometry class10.pptx

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

Math12 lesson 3

Math12 lesson 3

Trigonometry

Trigonometry

Rbse solutions for class 10 maths chapter 8 height and distance

Rbse solutions for class 10 maths chapter 8 height and distance

Angles-of-Elevation-and-Depression.pptx

Angles-of-Elevation-and-Depression.pptx

angle_of_elevation_depression cot2.pptx

angle_of_elevation_depression cot2.pptx

presentation_trigonometry.pptx

presentation_trigonometry.pptx

Important questions for class 10 maths chapter 9 some applications of trigono...

Important questions for class 10 maths chapter 9 some applications of trigono...

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- 3. What is Trigonometry? Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
- 4. In this topic we shall make use of Trigonometric Ratios to find the height of a tree, a tower, a water tank, width of a river, distance of ship from lighthouse etc.
- 7. Angle of Elevation The angle which the line of sight makes with a horizontal line drawn away from their eyes is called the angle of Elevation of aero plane from them. Angel of Elevation
- 8. • 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.
- 9. • Angle of Depression: The angle below horizontal that an observer must look to see an object that is lower than the observer. Note: The angle of depression is congruent to the angle of elevation (this assumes the object is close enough to the observer so that the horizontals for the observer and the object are effectively parallel).
- 10. Angle of Depression Horizontal Angel of Depression
- 12. Now let us Solve some problem related to Height and Distance
- 13. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. Find the height of the tower. . Let AB be the tower and the angle of elevation from point C (on ground) is 30°. In ΔABC, Therefore, the height of the tower is
- 14. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °. Sol:- It can be observed from the figure that AB is the pole. In ΔABC, Therefore, the height of the pole is 10 m.
- 15. . Let K be the kite and the string is tied to point P on the ground. In ΔKLP, Hence, the length of the string is
- 16. ,
- 17. . Height of tree = + BC Hence, the height of the tree is
- 20. 1 Tan 30 h 3 Tan 60 h 3 d From (1) d (1) d The angle of elevation of the top of a tower from a point At the foot of the tower is 300 . And after advancing 150mtrs Towards the foot of the tower, the angle of elevation becomes 600 .Find the height of the tower (2) 150 h 3 From ( 2 ) 3 (d h 150 ) h 30 60 Substituti ng ..the ..value ..of .. d .. 3 (h 3 3h 150 3h h 2h 150 h 150 ) 3 h 150 h 3 d 3 75 * 1 . 732 150 129 . 9 m
- 21. Questions based on trigonometry :• The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft. away from its base. Find the height of the flagpole. • Solution Step 1: Let’s first visualize the situation Step 2: Let ‘x’ be the height of the flagpole. STEP 3: From triangle ABC,tan48=x/18 Step 4: x = 18 × tan 48° = 18 × 1.11061… = 19.99102…» 20 Step 5: So, the flagpole is about 20 ft. high.
- 22. C A 50 D 45 A hoarding is fitted above a building. The height of the building is 12 m. When I look at the lights fitted on top of the hoarding, the angle of elevation is 500 and when I look at the top of the building from the same place, the angle is 450. If the height of the flat on each floor is equal to the height of the hoarding, the max floors on the building are? (Tan 500=1.1917) B ANSWER : Let AB denote the height of the building, Let AC denote the height of the hoarding on top of the building Thus, Tan500 = (12 + AC) ÷ 12 1.1917 = 1 + (AC ÷ 12) 1.1917 – 1 = AC ÷ 12 12 ÷ AC = 1 ÷ 0.1917 ~ 5