Question

The angle of elevation of a cloud from a point $60m$ above a 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.

• A. $30$
• B. $40$
• C. $60$
• D. $120$

Answer 1

Answer: (D)

$120$

$LetAO=H$
$CD=OB=60$
$A^{\prime }B=AB=60+H$
In $△AOD$,
$\tan {30}^{\circ }=\frac{AO}{OD}=\frac{H}{OD}$
$H=\frac{OD}{\sqrt{3}}$
$OD=\sqrt{3}H$
In $△A^{\prime }OD$,
$\tan 60=\frac{O{A}^{\prime }}{OD}=\frac{OB+B{A}^{\prime }}{OD}$

$\sqrt{3}=\frac{60+60+H}{\sqrt{3}H}=\frac{120+H}{\sqrt{3}H}$

$120+H=3H$
$2H=120m$
$H=60m$
Thus, Height of Cloud = $AB+A^{\prime }B=60+60=120m$