Question

If the angles of elevation of a tower from two points at a distance $a$ and $b(a>b)$ from its foot on the same side of the tower, have measures ${30}^o$ and ${60}^o$, then calculate the height of the tower.

Answer 1

$\tan 60=\frac{H}{6}\Rightarrow H=\sqrt{3}6$

$\tan 30=\frac{H}{a}\Rightarrow H=\frac{a}{\sqrt{3}}$

$H\times H=\sqrt{36}\times \frac{a}{\sqrt{3}}=ab$

$H=\sqrt{ab}$