Question

From a point 'P' on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point 'P' from the foot of the tower is:
1. 149 m
2. 156 m
3. 173 m
4. 200 m
5. 181 m

Answer 1

Correct Answer - Option 3 : 173 m

Given:

From a point 'P' on a level ground, the angle of elevation of the top of a tower = 30

Height of the tower = 100 m

Formula:

tan A = Perpendicular/Base

tan 30 = 1/√3

Calculation:

Let height of tower AB is 100 m.

The distance between P from foot of tower is PB.

In ΔPAB

tan 30 = AB/PB

⇒ 1/√3 = 100/PB

⇒ PB = 100√3

⇒ PB = 100 × 1.732

⇒ PB = 173.2

⇒ PB = 173 m (approx).

∴ The distance between P from foot of tower is 173 m.