Question

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

Options

• \[25\sqrt{3}\]

• \[50\sqrt{3}\]

• \[75\sqrt{3}\]

• 150        

Answer 1

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,

\[\angle\]ACB =\[\angle\]CAD = 30°  

In right ∆ABC,

\[\tan30° = \frac{AB}{BC}\]
\[ \Rightarrow \frac{1}{\sqrt{3}} = \frac{75 m}{BC}\]
\[ \Rightarrow BC = 75\sqrt{3} m\] 

Thus, the distance of the car from the base of the tower is 75 \[\sqrt{3}\]