Question

The angle of elevation of a cloud $C$ from a point $P,200m$ above a still lake is $30^{\circ }.$ If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ }$, then $PC$ (in $m$ ) is equal to :

• A. 400
• B. $400\sqrt{3}$
• C. 100
• D. $200\sqrt{3}$

Answer 1

Answer: (A)

Let $PA=x$
For $△APC$
$AC=\frac{PA}{\sqrt{3}}=\frac{x}{\sqrt{3}}$
$A{C}^1=AB+B{C}^1$
$A{C}^1=AB+BC$
$A{C}^1=400+\frac{x}{\sqrt{3}}$
From $\Delta C^{1}PA:A{C}^1=\sqrt{3}PA$
$\Rightarrow \left(400+\frac{x}{\sqrt{3}}\right)=\sqrt{3}x\Rightarrow x=(200)(\sqrt{3})$
from $\Delta APC:PC=\frac{2x}{\sqrt{3}}\Rightarrow PC=400$