Question

If the angle of elevation of a cloud from a point $P$ which is $25\text{m}$ above a lake be ${30}^{\circ }$ and the angle of depression of reflection of the cloud in the lake from $P$ be ${60}^{\circ }$, then the height of the cloud (in meters) from the surface of the lake is :

• A. $60$
• B. $50$
• C. $45$
• D. $42$

Answer 1

The correct option is B $50$


Let the height of cloud above the lake is $h$ metres.
$\tan {30}^{\circ }=\frac{h-25}{x}\cdots \left(1\right)$

$\tan {60}^{\circ }=\frac{h+25}{x}\cdots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,
$\sqrt{3}=\frac{h+25}{(h-25)\times \sqrt{3}}$

$\Rightarrow 3h-75=h+25$
$\Rightarrow h=50\text{m}$