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

The height of the cloud above the lake is equal to the length from the lake to its reflection.

In $△$ ABC',
$tan{60}^{\circ }=\frac{B{C}^{\prime }}{AB}=\frac{X+{400}^{\prime }}{AB}$
In $△$ ABC,
$tan{30}^{\circ }=\frac{X}{AB}$
$\Rightarrow X\sqrt{3}=\frac{X+400}{\sqrt{3}}$
$\Rightarrow X=200m$
Hence, the height of the cloud above the lake is 200 + 200 = 400 m