Question

A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height $7m$ from a point on the plane, the angle of elevation of the bottom and the top of flag-staff are ${30}^o$ and ${45}^o$ respectively. Find the height of the tower.

Answer 1

Let $AB$ be the tower whose height is $x$ m

$In△OBA$,

$\tan {30}^o=\frac{x}{OA}$

$OA=\sqrt{3}x$

$In△OCA$,

$\tan {45}^o=\frac{x+7}{OA}=\frac{x+7}{\sqrt{3}x}$

$\sqrt{3}x=x+7$

$x=\frac{7}{\sqrt{3}-1}$m is the height of tower