Question

A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole the angle of elevation of the top of the tower is ${60}^{\circ }$ and the angle of depression of the bottom of the tower is ${30}^{\circ }$. Find the height of the pole, if the height of the tower is 75 m.

Answer 1

$AC$ is pole.

$BD$ is tower.

Height of pole$=h$.

Height of tower$=h+d=75$

$\tan {60}^o=\frac{d}{OC}$

$\Rightarrow d=OC\sqrt{3}$

$\tan {30}^o=\frac{h}{OC}$

$\Rightarrow h=\frac{OC}{\sqrt{3}}$

$h+d=\frac{4OC}{\sqrt{3}}=75$

$\Rightarrow OC=\frac{75\sqrt{3}}{4}$

$\therefore$ Height of pole$=h=\frac{75}{4}=18.75m$