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 [CBSE 2013]
Suppose AB is the tower and C is the position of the car from the base of the tower.
It is given that, AB = 75 m
Now, $\angle A C B=\angle C A D=30^{\circ}$ (Alternate angles)
In right ∆ABC,
$\tan 30^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{75 \mathrm{~m}}{\mathrm{BC}}$
$\Rightarrow \mathrm{BC}=75 \sqrt{3} \mathrm{~m}$
Thus, the distance of the car from the base of the tower is $75 \sqrt{3} \mathrm{~m}$.
Hence, the correct answer is option C.