question_answer

A tower subtends an angle a  at a point A in the plane of its base and the angle of depression of the foot of the tower at a point l meters just above A is b. The height of the tower is    [MP PET 1990; RPET 1990]

A) \[l\,\,\tan \,\beta \,\cot \,\alpha \]

B) \[l\,\,\tan \,\alpha \,\cot \,\beta \]

C) \[l\,\,\tan \,\,\alpha \,\,\tan \,\beta \]

D) \[l\,\,\cot \,\,\alpha \,\,\cot \,\beta \]

Correct Answer: B

Solution :

From figure, we can deduce\[H=l\tan \alpha \cot \beta \].