Question

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of ${30}^{\circ }$, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be ${60}^{\circ }$. Find the time taken by the car to reach the foot of the tower from this point.

Answer 1

In $△ACD$

$\tan 60=\frac{AD}{CD}$

$AD=\sqrt{3}CD$ ----(1)

In $△ABD$

$\tan 30=\frac{AD}{BD}$

$AD=\frac{BD}{\sqrt{3}}$ ----(2)

By (1) and (2)

$\sqrt{3}CD=\frac{BD}{\sqrt{3}}$

$BD=3CD$

$BC+CD=3CD$

$BC=2CD$

$CD=\frac{1}{2}BC$

Time taken cover $BC=6\sec$

Time taken to cover $\frac{BC}{2}=3\sec$

Therefore, Time taken to reach to the foot ofthe tower