Question

The angle of elevation of a cloud from a point $h$ meters above the surface of a lake is ${30}^o$ and the angle of depression of its reflection is ${60}^o$. Then the height of the cloud above the surface of the lake is

• A. $h\sqrt{3}$
• B. $h$
• C. $\sqrt{2}h$
• D. $2h$

Answer 1

The correct option is D $2h$

$ED=E^{\prime }D=x$
$\frac{EB}{AB}=\tan {30}^o=\frac{1}{\sqrt{3}}\Rightarrow (x-h)=\frac{AB}{\sqrt{3}}...\left(1\right)$
Similarly $(x+h)=AB\sqrt{3}$
dividing (1) by (2)
$\frac{x-h}{x+h}=\frac{AB}{\sqrt{3}.\sqrt{3}.AB}=\frac{1}{3}$
$\Rightarrow x=2h$
$\therefore$ Height of cloud $=2h$