question_answer

From a point a meter above a lake the angle of elevation of a cloud is \[\alpha \] and the angle of depression of its reflection is \[\beta .\] The height of the cloud is

A) \[\frac{a\sin (\alpha +\beta )}{\sin (\alpha -\beta )}metre\]

B) \[\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )}metre\]

C) \[\frac{a\sin (\alpha -\beta )}{\sin (\alpha +\beta )}metre\]

D) None of these

Correct Answer: B

Solution :

[b] \[(H+a)cot\,b=(H-a)cot\,a\] using componendo and divdendo \[\Rightarrow H=\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )}\]