question_answer

From the bottom of a pole of height h, the angle of elevation of the top of a tower is \[\alpha \]and the pole subtends angle \[\beta \]at the top of the tower. The height of the tower is  [Roorkee 1988]

A) \[\frac{h\tan (\alpha -\beta )}{\tan (\alpha -\beta )-\tan \alpha }\]

B) \[\frac{h\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha }\]

C) \[\frac{\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha }\]

D) None of these

Correct Answer: B

Solution :

  \[d=H\cot \alpha \] \[d=(H-h)\cot (\alpha -\beta )\] \[\Rightarrow \] \[H\cot \alpha \] \[=(H-h)\cot (\alpha -\beta )\] or \[H=\frac{h\cot (\alpha -\beta )}{\cot (\alpha -\beta )-\cot \alpha }\].