Question

The shadow of a tower standing on a level plane is found to be $50m$ longer. When Sun's elevation ${30}^o$ than when it is ${60}^o$. Find the height of tower.

Answer 1

$\tan 60=\frac{h}{BC}$

$BC=\frac{h}{\sqrt{3}}$ ……….$\left(1\right)$

$\tan {30}^o=\frac{h}{BC+50}$

$\Rightarrow BC+50=\sqrt{3}h$

$BC=\sqrt{3}h-50$ ……….$\left(2\right)$

From $\left(1\right)$ & $\left(2\right)$

$\frac{h}{\sqrt{3}}=\sqrt{3}h-50$

$\Rightarrow h=3h-50\sqrt{3}$

$\Rightarrow 2h=50\sqrt{3}$

$\Rightarrow h=25\sqrt{3}$.