Question

A vertical tower $PQ$ subtends the same angle ${30}^o$ at each of two places $A$ and $B$, $60m$. apart on the ground, $AB$ subtends an angle ${120}^o$ at the foot of the tower. If $h$ is the height of the tower then $9h^2+h+1$ is equal to

Answer 1

$AP=PB=h\cot {30}^o=\sqrt{3}h$
$\cos {120}^o=\frac{3h^2+3h^2-{60}^2}{2.3h^2}=-\frac{1}{2}$
$\Rightarrow 9h^2={60}^2\Rightarrow h=20\Rightarrow 9h^2+h+1=3621$