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-

Answer: Option A

Solution

Answer: Option A

Solution:

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