Question

If the angle of elevation of a cloud from a point 200 m above a lake is ${30}^{\circ }$ and the angle of depression of the reflection of the cloud in the lake from the same point is ${60}^{\circ }$, then the height of the cloud above the lake is:

• A. 400 m
• B. 500 m
• C. 30 m
• D. 200 m

Answer 1

The correct option is A

400 m

In $△$ ABC',
$tan{60}^{\circ }=\frac{x+400}{AB}$
$\sqrt{3}=\frac{x+400}{AB}$
$AB=\frac{x+400}{\sqrt{3}}$___(i)

In $△$ ABC,
$tan{30}^{\circ }=\frac{x}{AB}$
$\frac{1}{\sqrt{3}}=\frac{x}{AB}$
$AB=x\sqrt{3}$ _______(ii)

Plugging the value of AB from equation (ii) in equation (i), we get
$\Rightarrow x\sqrt{3}=\frac{x+400}{\sqrt{3}}$
$\Rightarrow 3x=x+400$
$\Rightarrow x=200m$
Hence, the height of the cloud above the lake is
200 + 200 = 400 m