devarshi-dt-logo

Question:

The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m.) is:

50√3

75√3

150

25√3

Solution:

In right-angled triangle ABC, the ∠ACB = 30° (Angle of depression of a car) and the tower is 75 m high.
Let the distance of the car from the base of the tower be x m.
Then tan 30° = AB/BC = 75/x
⇒ 1/√3 = 75/x
⇒ x = 75√3 m