Question

An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be $30^{\circ }.$ After $3$ minutes this angle becomes $60^{\circ }.$ If the time taken by the car to reach the tree is $\alpha$ (in min.), then $4\alpha$ is equal to

Answer 1

Answer: 6

$d=hcot30^{\circ }-hcot60^{\circ }$ and time $=3min$

$\therefore$ Speed $=\frac{h\left(cot30^{\circ }-cot60^{\circ }\right)}{3}$ per minute
It will travel distance $hcot60^{\circ }in$
$\frac{hcot60^{\circ }\times 3}{h\left(cot30^{\circ }-cot60^{\circ }\right)}=1.5$ minute
$4\alpha =6$