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

Answer 1

The correct option is A 200 m

In $△AB{C}^{\prime }$,

$\tan {60}^{\circ }=\frac{x+400}{AB}$

$AB=\frac{x+400}{\tan {60}^{\circ }}=\frac{x+400}{\sqrt{3}}$

In $△ABC$,

$\tan {30}^{\circ }=\frac{x}{AB}$

$AB=\frac{x}{\tan {30}^{\circ }}=x\sqrt{3}$

$\because AB=AB$

$\Rightarrow x\sqrt{3}=\frac{x+400}{\sqrt{3}}$

$\Rightarrow x\times \sqrt{3}\times \sqrt{3}=x+400$

$\Rightarrow 3x=x+400$

$\Rightarrow 2x=400$

$\Rightarrow x=200m$

Hence, the height of the cloud above the lake is

$200+200=400m$