Chapter 9 — Some Applications of Trigonometry

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

• Line of sight and its angles — The line of sight runs from the observer's eye to an object. When it rises above the horizontal it forms an angle of elevation; when it drops below, an angle of depression.
• Measuring without touching — By placing these angles inside right triangles and applying ratios like tan, sin, and cot, heights of poles, chimneys, and buildings and widths of rivers can be found without any physical measurement.
• Two-triangle problems — Many real situations need two right triangles together — for instance, finding both a flagstaff's height and a building's distance from a viewpoint — solved by combining the ratios from each triangle.

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.