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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.
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Trigonometry is a branch of mathematics that studies triangles and the relationships between sides and angles. It uses trigonometric ratios to calculate heights, distances, and other measurements that cannot be directly observed. The angle of elevation is formed between an observer's line of sight and the horizontal when looking up at an object. The angle of depression is formed when an observer looks down, between the line of sight and the horizontal. Both can be used with trigonometric functions to determine 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.
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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.
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This document discusses trigonometry and introduces Hipparchus of Bithynia as the Greek mathematician who systematized trigonometry. It defines the trigonometric functions of sine, cosine, and tangent using the mnemonic SOH-CAH-TOA. It also defines angle of elevation and angle of depression and provides examples of calculating trigonometric functions in right triangles. Finally, it gives an assignment involving using trigonometric functions to find the height of a hot air balloon.
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.
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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
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.
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.
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Maths ppt 2016 .fb
Trigonometry is a branch of mathematics that studies triangles and the relationships between sides and angles. It uses trigonometric ratios to calculate heights, distances, and other measurements that cannot be directly observed. The angle of elevation is formed between an observer's line of sight and the horizontal when looking up at an object. The angle of depression is formed when an observer looks down, between the line of sight and the horizontal. Both can be used with trigonometric functions to determine unknown measurements.
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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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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.
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This document discusses trigonometry and introduces Hipparchus of Bithynia as the Greek mathematician who systematized trigonometry. It defines the trigonometric functions of sine, cosine, and tangent using the mnemonic SOH-CAH-TOA. It also defines angle of elevation and angle of depression and provides examples of calculating trigonometric functions in right triangles. Finally, it gives an assignment involving using trigonometric functions to find the height of a hot air balloon.
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.
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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
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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.
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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.
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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.
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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.
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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.
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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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A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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.
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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.
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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.
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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.
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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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A powerpoint presentation on the topic applications of trigonometry with an introduction to trigonometry.
By Spandan Bhattacharya
Student
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.
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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.
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.
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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.
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.
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
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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.
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This document discusses trigonometric ratios and identities. It defines the trigonometric ratios of sine, cosine and tangent for an acute angle A in a right triangle ABC. It also defines cosecant, secant and cotangent. It provides the reciprocal identities and values of the trigonometric ratios for common angles. It lists formulas for trigonometric functions of complementary angles and the main trigonometric identities along with steps for proving identities.
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.
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Clinometers are used in many professions to measure slopes and inclines. Geologists, surveyors, skiers, sailors, and cave surveyors use clinometers to measure heights, slopes, cloud heights, and map underground cave systems. City planners also use clinometers to ensure that roads and sidewalks do not exceed a 10% gradient, as steeper slopes can be dangerous and increase pollution from vehicles. The document provides examples of how clinometers are used in various fields and describes an activity where students measure hill gradients to determine if roads should be built.
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Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview
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This document provides an introduction to trigonometry, including its history and key concepts. Trigonometry deals with right triangles and relationships between their sides. Important concepts discussed include the trigonometric ratios (sine, cosine, tangent etc.), Pythagorean theorem, and applications to fields like construction, astronomy, and engineering. An example problem demonstrates using trigonometric functions to calculate the height of a flagpole given the angle of elevation and distance from the base.
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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.
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.
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Trigonometry, Applications of Trigonometry CBSE Class X Project
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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
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.
Math12 lesson3
1. Solving right triangles involves sketching the triangle, identifying given and unknown parts, and using trigonometric functions, the Pythagorean theorem, or angle relationships to calculate unknowns.
2. Angles of elevation are formed between an observer's line of sight above the horizontal, while angles of depression are below the horizontal. These can be used to calculate heights or distances.
3. Bearing is the acute angle from north or south, while course is the clockwise angle from north along the line of travel. These specify directions.
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- 2. What is Trignometry? Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
- 3. In this topic we shall make use of Trignometric Ratios to find the height of a tree,a tower,a water tank,width of a river,distance of ship from lighthouse etc.
- 6. 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 aeroplane from them.
- 7. Angel of Elevation Angel of Elevation
- 8. Angel of Depression If the pilot of the aeroplane looks downwards at any object on the ground then the Angle between his line of sight and horizontal line drawn away from his eyes is called Angel of Depression
- 9. Angle of Depression Horizontal Angel of Depression
- 11. Now let us Solve some problem related to Height and Distance
- 12. 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
- 13. 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.
- 14. 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
- 15. ,
- 16. Height of tree = . + BC Hence, the height of the tree is