Question

One side of a road, there is a tower and on other side, a house is situated. The angle of depression from the top of a tower to top and bottom of house are ${45}^0$ and ${60}^o$ respectively. Find the height of tower.

Answer 1

Let $AB=H$

$CD=h$

$AC=b$

$\therefore \tan {60}^0=\frac{H}{b}$

$\Rightarrow H=b\sqrt{3}$

And $\tan {45}^0=\frac{H-h}{b}$

$\Rightarrow b=H-h$

$\Rightarrow \frac{H}{\sqrt{3}}=H-h$

$\Rightarrow h=H(1-\frac{1}{\sqrt{3}})$

$\Rightarrow H=\frac{\sqrt{3}h}{\sqrt{3}-1}$ where $h$ is the height of the house.