Question

The angle of elevation of a cloud from a point $60m/s$ above the surface of the water a lake is ${30}^o$ and the angle of depression of its shadow from the same point in water of lake is ${60}^o$. Find the height of the cloud from the surface of water.

Answer 1

$DC=H.$

$DB=D^{\prime }B=(60+H)$

In $△ECD\tan {30}^0=\frac{DC}{EC}=\frac{H}{EC}$

$EC=\sqrt{3}H$

In $△ECD\tan {60}^0=\frac{D^{\prime }C}{EC}=\frac{D^{\prime }B+BC}{EC}=\frac{60+H+60}{\sqrt{3}H}$

$3H=120+H$

$H=60m$

Height of cloud $=60+60=120m.$