question_answer

The base of a cliff is circular. From the extremities of a diameter of the base the angles of elevation of the top of the cliff are 30o and\[{{60}^{o}}\]. If the height of the cliff be 500 metres, then the diameter of the base of the cliff is

A) \[1000\,\sqrt{3}\,m\]

B) \[2000/\sqrt{3}\,m\]

C) \[1000/\sqrt{3}\,m\]

D) \[2000\sqrt{2}\,m\]

Correct Answer: B

Solution :

\[{{d}_{2}}=h\cot {{30}^{o}}=500\sqrt{3},\,{{d}_{1}}=\frac{500}{\sqrt{3}}\] Diameter \[D=500\sqrt{3}+\frac{500}{3}\sqrt{3}=\frac{2000}{\sqrt{3}}m\].