Question

From the top a tower of height $50m$, angle of depression of the top and bottom of a pole are ${30}^o$ and ${45}^o$. Find height of pole.

Answer 1

REF.Image

In $△ADE$

$tan{45}^{\circ }=\frac{AE}{DE}=\frac{50}{x}$

$1=\frac{50}{x}$

$x=50m$

$\Rightarrow$ In $△ABC\Rightarrow tan{30}^{\circ }=\frac{AC}{BC}=\frac{50-H}{x}$

$\frac{1}{\sqrt{3}}=\frac{50-H}{50}$

$H=50\left(\frac{\sqrt{3}-1}{\sqrt{3}}\right)=21.13m$

$\therefore$ Height of pole $\Rightarrow 21.13m$