# NCERT Class 10 Mathematics Chapter 9 Some Applications of Trigonometry: Summary, Concepts, and Revision Notes | SwaVid This chapter, 'Some Applications of Trigonometry', builds upon your knowledge of trigonometric ratios to solve real-world problems involving heights and... Canonical: https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry Source: https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry # Some Applications of Trigonometry ## Concepts in this chapter ## The ideas this chapter keeps returning to ## Where this chapter usually trips people up ## Find the gaps before this chapter finds them for you. ## Related chapters ### Line of Sight Chapter 9 · Class 10 Mathematics This chapter, 'Some Applications of Trigonometry', builds upon your knowledge of trigonometric ratios to solve real-world problems involving heights and distances. It focuses on applying the concepts of angles of elevation and depression to practical scenarios, often without needing to directly measure heights or distances. Your study route Key topics The line of sight is the line drawn from the eye of an observer to the object being viewed. It forms the hypotenuse of the right-angled triangle in most problems. Example Figure 9.1 (The line from the observer's eye to the top of the minar) Watch out Students sometimes confuse the line of sight with the horizontal line or the vertical height. The line of sight is the line drawn from the eye of an observer to the object being viewed. It forms the hypotenuse of the right-angled triangle in most problems. Tap the card for an example Example Figure 9.1 (The line from the observer's eye to the top of the minar) Why it matters It is the fundamental reference for defining angles of elevation and depression, forming the hypotenuse of the right triangle used for calculations. Watch out Students sometimes confuse the line of sight with the horizontal line or the vertical height. Ask at home Ask your child to describe what the 'line of sight' is when they look at the top of a tree from the ground. In this chapter, students learn to apply trigonometric ratios (sine, cosine, tangent) to determine heights and distances of various objects. The core concepts introduced are the 'line of sight', 'angle of elevation', and 'angle of depression'. The line of sight is the line from the observer's eye to the object being viewed. When an observer looks up at an object, the angle formed between the line of sight and the horizontal level is called the angle of elevation. Conversely, when an observer looks down at an object, the angle formed between the line of sight and the horizontal level is called the angle of depression. Students will practice drawing appropriate diagrams for given situations, identifying right-angled triangles, and then using the correct trigonometric ratios to find unknown lengths or angles. This chapter emphasizes problem-solving skills and the practical utility of trigonometry in fields like engineering, navigation, and surveying. Chapter summary In this chapter, students learn to apply trigonometric ratios (sine, cosine, tangent) to determine heights and distances of various objects. The core concepts introduced are the 'line of sight', 'angle of elevation', and 'angle of depression'. The line of sight is the line from the observer's eye to the object being viewed. When an observer looks up at an object, the angle formed between the line of sight and the horizontal level is called the angle of elevation. Conversely, when an observer looks down at an object, the angle formed between the line of sight and the horizontal level is called the angle of depression. Students will practice drawing appropriate diagrams for given situations, identifying right-angled triangles, and then using the correct trigonometric ratios to find unknown lengths or angles. This chapter emphasizes problem-solving skills and the practical utility of trigonometry in fields like engineering, navigation, and surveying. What you should learn Keep these close The line of sight is the line from the observer's eye to the object. The angle of elevation is formed when looking up, between the line of sight and the horizontal. The angle of depression is formed when looking down, between the line of sight and the horizontal. Always draw a clear, labeled diagram for each problem. Identify the right-angled triangle(s) in your diagram. Correctly label the known angles, known sides, and the unknown quantity to be found. Choose the appropriate trigonometric ratio (sin, cos, tan) based on the sides and angles involved. Remember that the angle of depression from point A to point B is equal to the angle of elevation from point B to point A (alternate interior angles). For problems with two triangles, look for a common side to relate them. Use the given values of trigonometric ratios (e.g., tan 30°, sin 60°) accurately. Pay attention to units and ensure consistency throughout the problem. Practice solving a variety of problems to build confidence and understanding. Common confusions It is easy to think The angle of depression is measured from the vertical line. The clearer idea The angle of depression is always measured from the horizontal line, downwards to the line of sight. It is never measured from the vertical. It is easy to think Confusing the angle of elevation with the angle of depression, or assuming they are always the same in any context. The clearer idea Angle of elevation is for looking up, angle of depression for looking down. They are equal only when they are alternate interior angles formed by parallel horizontal lines and a transversal line of sight. It is easy to think Incorrectly identifying the 'opposite', 'adjacent', and 'hypotenuse' sides relative to the angle in the right-angled triangle. The clearer idea The hypotenuse is always opposite the right angle. The 'opposite' side is across from the reference angle, and the 'adjacent' side is next to the reference angle (not the hypotenuse). It is easy to think Not drawing a diagram or drawing an inaccurate diagram, leading to incorrect problem setup. The clearer idea Drawing a neat, labeled diagram is the most crucial first step. It helps visualize the problem and correctly apply trigonometric ratios. Always include the horizontal line for angles. Before you push ahead Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns. Keep exploring Class 10 Source - Define and correctly identify the line of sight, angle of elevation, and angle of depression in various scenarios. - Draw accurate diagrams representing real-world situations involving heights and distances. - Apply appropriate trigonometric ratios (sin, cos, tan) to solve problems involving single right-angled triangles. - Solve more complex problems involving two right-angled triangles to find unknown heights or distances. - Understand the practical applications of trigonometry in determining heights and distances without direct measurement. - Define and correctly identify the line of sight, angle of elevation, and angle of depression in various scenarios. - Draw accurate diagrams representing real-world situations involving heights and distances. - Apply appropriate trigonometric ratios (sin, cos, tan) to solve problems involving single right-angled triangles. - Solve more complex problems involving two right-angled triangles to find unknown heights or distances. - Understand the practical applications of trigonometry in determining heights and distances without direct measurement. - NCERT Class 10 Mathematics textbook: Mathematics : Chapter 9: Some Applications of Trigonometry ## Key Links - [NCERT Mathematics](https://swavid.com/maths) - [Class 10](https://swavid.com/maths/class/10) - [Start with concepts](https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry) - [Check a prerequisite](https://swavid.com/learning-debt-identifier) - [Concepts](https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry) - [Practice](https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry/practice-questions) - [NCERT Solutions](https://swavid.com/maths/class/10/chapter/some-applications-of-trigonometry/ncert-solutions) - [Find the gaps before this chapter](https://swavid.com/learning-debt-identifier) - [Learn this chapter adapted to you](https://swavid.com/learning-style-test) - [Previous chapter 8 . 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