Question

If the angle of elevation of a cloud from a point $P$ which is $25\, m$ 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)

50

Answer 2

tan 30? = $\frac{}{} \, \Rightarrow \, y = \sqrt{3} x \, \, \, \, \, \, \, \, \, \, \, \, ...(i)$
$tan 60^{\circ} \, \, =\frac{25+x+25}{y}$
$\Rightarrow \, \, \sqrt{3} y \, = \, 50 + x$
$\Rightarrow \, \, 3x = 50 + x$
$\Rightarrow \, \, x \, = \, 25 m$
$\therefore \,$ Height of cloud from surface = $25 + 25 = 50\,m$