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:

Options

• (A)`25sqrt3` 

• (B)`50sqrt3`

• (C)`75sqrt3`

• (D) 150

Answer 1

Let AB be the tower of height 75 m.

∠ABD = ∠ACB = 30°

Suppose C be the position of the car from the base of the tower.

In right ΔABC,

`cot 30^o=(AC)/(AB)`

`rArrAC=AB\ cot30^o`

`rArrAC=75mxxsqrt3`

`rArrAC=75sqrt3 m`

Thus, the distance of the car from the base of the tower is `75sqrt3m`.