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

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