If the angle of elevation of a cloud from a point 200 m above a lake is 30∘

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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:

Options:

A . 400 m

B . 500 m

C . 30 m

D . 200 m

Answer: Option A
:
A

In $△$ ABC',
$t a n 60^{\circ} = \frac{x + 400}{A B}$
$\sqrt{3} = \frac{x + 400}{A B}$
$A B = \frac{x + 400}{\sqrt{3}}$ ___(i)
In $△$ ABC,
$t a n 30^{\circ} = \frac{x}{A B}$
$\frac{1}{\sqrt{3}} = \frac{x}{A B}$
$A B = x \sqrt{3}$ _______(ii)
Plugging the value of AB from equation (ii) in equation (i), we get
$\Rightarrow x \sqrt{3} = \frac{x + 400}{\sqrt{3}}$
$\Rightarrow 3 x = x + 400$
$\Rightarrow x = 200 m$
Hence, the height of the cloud above the lake is
200 + 200 = 400 m

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