Question

The angle of elevation of the cloud from a point 60 m above lake is ${30}^{\circ }$ and the angle of depression of the reflection of the cloud in the lake is ${60}^{\circ }$ . Find the height of the cloud from the surface of lake.

Answer 1

Let $AO=H$

$\Rightarrow$$CD=OB=60m$

$\Rightarrow$$A^{\prime }B=AB=60+H$

$\Rightarrow$In $△AOD$

$\Rightarrow$$\tan {30}^{\circ }=\frac{AO}{OD}=\frac{H}{OD}$

$\Rightarrow H=OD/\sqrt{3}$

$\Rightarrow$In $△A^{\prime }OD$

$\Rightarrow$$\tan {60}^{\circ }=\frac{A^{\prime }O}{OD}=\frac{OB+AB}{OD}$

$\Rightarrow \sqrt{3}=(120+H)/\sqrt{3}H$

$\Rightarrow H=60m$

Height of the cloud from the surface of lake $=60+60=120m$