Question

A man from the top of a $300$ metres high tower sees a car moving towards the tower at an angle of depression $30^{\circ }$. After some time, the angle of depression becomes $60^{\circ }$. If the distance (in meters) travelled by the car during this time is $k\sqrt{3}$, then find $k$.

Answer 1

Answer: 200.00

As $\tan 60^{\circ }=\frac{300}{b}$
$\Rightarrow b=\frac{300}{\sqrt{3}}$
Again, $\tan 30^{\circ }=\frac{300}{b+x}$
$\Rightarrow b+x=300\sqrt{3}$
$\Rightarrow x=300\sqrt{3}-\frac{300}{\sqrt{3}}$
$=\frac{600}{\sqrt{3}}=200\sqrt{3}$