# 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
AB is a tower and AB = 75 m From A, the angle of depression of a car C on the ground is 30° $\begin{array}{l}\text{Let distance BC}=x\\ \text{Now in right }\triangle\text{ACB},\\ \tan\theta=\frac{\text{AB}}{\text{BC}}\\ \Rightarrow\tan30^{\circ}=\frac{75}{x}\\ \Rightarrow\frac{1}{\sqrt{3}}=\frac{75}{x}\\ \Rightarrow x=75\sqrt{3}\text{m}\\ \therefore\text{BC}=75\sqrt{3}\text{m}\end{array}$