question_answer

The angle of elevation of a stationary cloud from a point 2500 m above a lake is\[{{15}^{o}}\]and the angle of depression of its reflection in the lake is\[{{45}^{o}}\]. The height of cloud above the lake level is [IIT 1976]

A) \[2500\,\sqrt{3}\,metres\]

B) 2500 metres

C) \[500\,\sqrt{3}\,metres\]

D) None of these

Correct Answer: A

Solution :

\[(H-h)\cot {{15}^{o}}=(H+h)\cot {{45}^{o}}\] or \[H=\frac{h\,(\cot {{15}^{o}}+1)}{(\cot {{15}^{o}}-1)}\] Since \[h=2500\] and substitute \[\cot {{15}^{o}}=2+\sqrt{3}\],we get,  \[H=2500\,\sqrt{3}\].