Question

The base of a cliff is circular. From the extremities of a diameter of the base, angles of elevation of the top of the cliff are ${30}^{\circ }$ and ${60}^{\circ }$. If the height of the cliff be $500\text{m}$, then the diameter of the base of the cliff is

• A. $\frac{2000}{\sqrt{3}}\text{m}$
• B. $\frac{1000}{\sqrt{3}}\text{m}$
• C. $\frac{2000}{\sqrt{2}}\text{m}$
• D. $1000\sqrt{3}\text{m}$

Answer 1

Answer: (A)

$\frac{2000}{\sqrt{3}}\text{m}$

In $△AEC$,
$\tan {60}^o=\frac{500}{d_1}$
$\Rightarrow \sqrt{3}=\frac{500}{d_1}$
$\Rightarrow d_1=\frac{500}{\sqrt{3}}\text{m}$
and in $△BEC$,
$\tan {30}^o=\frac{500}{d_2}$
$\Rightarrow d_2=500\sqrt{3}\text{m}$
$\therefore$ Required diameter $=d_1+d_2$
$=\frac{500}{\sqrt{3}}+500\sqrt{3}=\frac{2000}{\sqrt{3}}\text{m}$