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

A. 25 $$\sqrt 3 $$

B. 50 $$\sqrt 3 $$

C. 75 $$\sqrt 3 $$

D. 150

Answer: Option C

Solution(By Examveda Team)

AB is a tower and AB = 75 m
From A, the angle of depression of a car C
on the ground is 30°

$$\eqalign{ & {\text{Let distance }}BC = x \cr & {\text{Now in right }}\Delta ACB, \cr & \tan \theta = \frac{{AB}}{{BC}} \cr & \Rightarrow \tan {30^ \circ } = \frac{{75}}{x} \cr & \Rightarrow \frac{1}{{\sqrt 3 }} = \frac{{75}}{x} \cr & \Rightarrow x = 75\sqrt 3 \,m \cr & \therefore BC = 75\sqrt 3 \,m \cr} $$