Question

The angle of elevation of a cloud $C$ from a point $P , 200 m$ 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 $P C$ (in $m$ ) is equal to :

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

Answer 1

Answer: (A)

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