question_answer

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

A) \[2500\sqrt{3}\] meters

B) \[2500\] meters

C) \[500\sqrt{3}\] meters

D) None of these

Correct Answer: A

Solution :

[a] \[(H-h)cot15{}^\circ =(H+h)cot45{}^\circ \] or \[H=\frac{h(cot15{}^\circ +1)}{(cot15{}^\circ -1)}\] Since \[h=2500\]and substitute \[\cot 15{}^\circ =2+\sqrt{3},\] we get \[H=2500\sqrt{3}\]