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 \[30{}^\circ \] and\[60{}^\circ \]. If the height of the cliff be 500 meters, 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 :

[b] \[{{d}_{2}}=h\cot 30{}^\circ =500\sqrt{3},\] and \[{{d}_{1}}=\frac{500}{\sqrt{3}}\] Diameter \[d=500\sqrt{3}+\frac{500}{3}\sqrt{3}=\frac{2000}{\sqrt{3}}m\]