Question

A tower subtends an angle $\alpha$ at a point$A$ on the same level as the foot of the tower $B$ is a point vertically above $A$ and $AB=h$ metres. The angle of depression of the foot of the tower from $B$ is $\beta$. The height of the tower is

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

Answer 1

The correct option is A $h\tan \alpha \cot \beta$

$\tan \alpha =\frac{h_1}{d}$
$\tan \beta =\frac{h}{d}$
$\frac{\tan \alpha }{\tan \beta }=\frac{h_1}{h}$

$h_1=h\tan \alpha \cot \beta$