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

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

$\therefore $ Speed $=\frac{h \left(cot 30 ^\circ - cot 60 ^\circ \right)}{3}$ per minute
It will travel distance $hcot60^\circ in$
$\frac{h cot 60 ^\circ \times 3}{h \left(cot 30 ^\circ - cot 60 ^\circ \right)}=1.5$ minute
$4\alpha =6$