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)

400

Answer 2

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 $\Delta APC : PC =\frac{2 x }{\sqrt{3}} \Rightarrow PC =400$