Chapter 9 — Some Applications of Trigonometry

NCERT Class 10 Maths Chapter 9 covers Some Applications of Trigonometry, teaching students how to use trigonometric ratios to find heights of towers, buildings, and other objects, and distances between them, using the concepts of angle of elevation and angle of depression.

Chapter 9 of NCERT Class 10 Mathematics applies trigonometric ratios to real-life situations involving heights and distances. It introduces the line of sight, angle of elevation (formed when looking upward at an object above the horizontal), and angle of depression (formed when looking downward at an object below the horizontal). Using tan, sin, cot, and related ratios in right-angled triangles, students learn to calculate the height of towers, poles, chimneys, and multi-storeyed buildings, as well as the width of rivers and distances between objects, without physically measuring them.

1. 01The line of sight is the line drawn from the observer's eye to the object being viewed.
2. 02The angle of elevation is formed when the line of sight is above the horizontal level (observer looks up).
3. 03The angle of depression is formed when the line of sight is below the horizontal level (observer looks down).
4. 04Trigonometric ratios such as tan, sin, and cot are used in right-angled triangles to calculate unknown heights and distances.
5. 05A tower 15 m away with an angle of elevation of 60° has a height of 15√3 m, calculated using tan 60° = √3.
6. 06Problems often involve two right triangles simultaneously, such as finding both the height of a flagstaff and the distance of a building from a point.