Question

A tower subtends at angle $\theta$ at a point P on the same level as the foot of the tower and from a point h m above P the depression of the foot of the tower is $\alpha$ . The height of the tower is (in m)

• A. $h$ $\tan \theta \tan \alpha$
• B. $h$ $cot\theta \cot \alpha$
• C. $h$ $\tan \theta \cot \alpha$
• D. $\cot \theta \tan \alpha$

Answer 1

The correct option is C $h$ $\tan \theta \cot \alpha$

Here, $\tan \theta =\frac{H}{x}\Rightarrow x=H\cot \theta .....\left(1\right)\tan \alpha =\frac{h}{x}\Rightarrow x=h\cot \alpha .....\left(2\right)$

Equating (1) and (2)

$H\cot \theta =h\cot \alpha \Rightarrow H=h\cot \alpha \tan \theta$

Therefore, Answer is $h\cot \alpha \tan \theta$