Question

The angle of elevation of a cloud from a point $100m$ above a lake is ${30}^o$ and the angle of depression of its reflection in the lake is ${60}^o$. Find the height of the cloud.

• A. $340m$
• B. $200m$
• C. $400m$
• D. $780m$

Answer 1

The correct option is B $200m$

Let the perpendicular distance of the cloud from the point of reference be h.
Let he distance between the foot of the perpendicular to the point be y.
Hence
$\tan {30}^0=\frac{h}{y}=\frac{1}{\sqrt{3}}$
Hence
$y=\sqrt{3}h$
Now image is equidistant from the object since the lake behaves as a plane mirror.
Hence
$\tan {60}^0=\sqrt{3}=\frac{h+100+100}{y}$
Hence
$\sqrt{3}y=h+200$
Or
$3h=h+200$
Or
$h=100m$
Hence height of the cloud from the ground will be
$h+100=200m$