CBSE · Class 6-12

Class 10 · Mathematics (Basic)

Unit 9 · Class 10Mathematics (Basic)

Some Applications of Trigonometry

Real-life problems on heights and distances using angles of elevation and depression.

Lessons

6 concepts

1
Angle of Elevation
When you look up at an object above the horizontal, the angle between your line of sight and the horizontal is the angle of elevation. As the observer moves closer, the elevation increases; as they move away, it decrease…
2
Angle of Depression
When looking down at an object below the horizontal, the angle from the horizontal to the line of sight (downward) is the angle of depression. By alternate angles, the angle of depression from top equals the angle of ele…
3
Setting Up the Problem
Sketch a right triangle: vertical leg is the object's height, horizontal leg is the distance from the observer, hypotenuse is the line of sight. Use the appropriate ratio ( $\tan, \sin,$ or $\cos$ ) based on which sides yo…
4
Two-Observer or Two-Object Problems
When a single object is seen from two points, form two right triangles sharing a common side (usually the height). Set up equations from the two angles and solve simultaneously to find both the unknown height and distanc…
5
Common Angles and Values
Most problems use $\theta \in \{30, 45, 60\}$ so that $\tan\theta$ takes clean values. Being fluent in $\tan 30 = 1/\sqrt 3$ , $\tan 45 = 1$ , $\tan 60 = \sqrt 3$ is essential.
6
Sanity Checking Answers
Heights and distances are positive real numbers. A steeper angle means the object appears farther up for the same distance, i.e. more height. Cross-check that your answer respects the geometry (e.g., height not exceeding…

Skills to practise

Skill · medium

Some Applications of Trigonometry — Practice