Question

If the angle of elevation of a cloud from a point P which is $25$ m above a lake be ${30}^0$ and the angle of depression of reflection of the cloud in the lake from P be ${60}^0$, 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

The correct option is B $50$

$tan{30}^0=\frac{x}{y}\Rightarrow y=\sqrt{3}x$ .......... (i)

$tan{60}^0=\frac{25+x+25}{y}$

$\Rightarrow \sqrt{3}y=50+x$

$\Rightarrow 3x=50+x$

$\Rightarrow x=25m$

$\therefore$ Height of cloud from surface = 25 + 25 = 50 m