The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is.
A. 200 m B. 300 m C. 400 m D. 600 m Answer: Option AShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{Let AC}=\ \text{H}\ \text{metre}\\
\text{OA}=\text{a}\ \text{metre}\\
\text{tan}\ 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{\text{H}}{a}\\
\tan 60^{\circ}=\sqrt{3}=\frac{H+200+200}{a} \\
\Rightarrow \frac{H+400}{\sqrt{3} H}=\sqrt{3} \\
\Rightarrow H+400=3 H \\
\Rightarrow 2 H=400 \mathrm{~m} \\
\Rightarrow H=200 \mathrm{~m}
\end{array}$
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