Question

The angle of elevation of a stationary cloud from a point $25m$ above a lake is ${15}^o$ and the angle of depression of its image in the lake is ${45}^o$. The height of the cloud above the lake level is

• A. $25m$
• B. $25\sqrt{3}m$
• C. $50m$
• D. $50\sqrt{3}m$

Answer 1

The correct option is B $25\sqrt{3}m$

$\tan 15°=2-\sqrt{3}=\frac{x}{x+50}\Rightarrow x=\frac{-50(2-\sqrt{3})}{1-\sqrt{3}}Now,x+25\Rightarrow \frac{-50(2-\sqrt{3})}{1-\sqrt{3}}+25=25\sqrt{3}$

Therefore, Height of Cloud is $25\sqrt{3}$