Question

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

• A. 42
• B. 50
• C. 45
• D. 60

Answer 1

Answer: (B)

tan 30° = $\frac{}{}\Rightarrow y=\sqrt{3}x...(i)$
$tan60^{\circ }=\frac{25+x+25}{y}$
$\Rightarrow \sqrt{3}y=50+x$
$\Rightarrow 3x=50+x$
$\Rightarrow x=25m$
$\therefore$ Height of cloud from surface = $25+25=50m$