Question

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30^o and the angle of depression of reflection of the cloud in the lake from P be 60^o, then the height of the cloud (in meters) from the surface of the lake is :

• A. 45
• B. 42
• C. 50
• D. 60

Hint:

Let the cloud be h m above the lake; its image is h m below the lake surface. Use \(\tan30^\circ\) and \(\tan60^\circ\) with the same horizontal distance.

Answer 1

The Correct Option is C

Let the cloud be at height h m above the lake and let the horizontal distance from P to the cloud be d.
Cloud above P: \(h-25\). Image of the cloud is h below the lake surface, i.e. \(h+25\) below P.
Elevation: \(\tan30^\circ=\frac{h-25}{d}\Rightarrow d=\sqrt3\,(h-25)\).
Depression of image: \(\tan60^\circ=\frac{h+25}{d}\Rightarrow d=\frac{h+25}{\sqrt3}\).
Equate: \(3(h-25)=h+25\Rightarrow 2h=100\Rightarrow h=50\) m.
Answer: (3) 50