Question

A tower subtends an angle α 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 β. The height of the tower is

• A. $l \tan \beta \cot \alpha$
• B. $l \tan \alpha \cot \beta$
• C. $l \tan \alpha \tan \beta$
• D. $l \cot \alpha \cot \beta$

Answer 1

Answer: (B)

$l \tan \alpha \cot \beta$

Answer 2

$\frac { H } { O A } = \tan \alpha \Rightarrow H = O A \tan \alpha$ ……..(i)

$\frac { l } { O A } = \tan \beta \Rightarrow O A = l \cot \beta$ ..…..(ii)

From (i) and (ii) $H = l \tan \alpha \cot \beta$