The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is-

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let, }}AC = H{\text{ }}m \cr & OA = {\text{ }}a{\text{ }}m \cr & \tan {\text{ }}{30^ \circ } = \frac{1}{{\sqrt 3 }} = \frac{H}{a} \cr} $$
$$\tan {60^ \circ } = \sqrt 3 $$    $$ = \frac{{H + 200 + 200}}{a}$$
$$\eqalign{ & \Rightarrow \frac{{H + 400}}{{\sqrt 3 H}} = \sqrt 3 \cr & \Rightarrow H + 400 = 3H \cr & \Rightarrow 2H = 400\,m \cr & \Rightarrow H = 200\,m \cr} $$
Height of cloud above lake = 200 m