Question

A vertical tower stands on a horizontal plane and is surmounted by a flagsataff of height $5m$. From a point on a ground, the angles of elevation of the top and bottom of the flagstaff are ${60}^o$ and ${30}^o$ respectively. Find the height of the tower and the distance of the point from the tower. (Take $\sqrt{3}=1.732$)

Answer 1

Let, $AB=hm$ be the height of the tower

$BC=5m$ be the height of the flagstaff

$OA=xm$ be the distance of the point from the tower.

From, $△OAB$

$\tan {30}^{\circ }=\frac{h}{x}$

$⟹\frac{1}{\sqrt{3}}=\frac{h}{x}$

$⟹x=\sqrt{3}h$............(i)

From, $△OAC$

$\tan {60}^{\circ }=\frac{5+h}{x}$

$⟹\sqrt{3}=\frac{5+h}{x}$

$⟹\sqrt{3}x=5+h$............(ii)

$⟹\sqrt{3}\left(\sqrt{3}h\right)=5+h$

$⟹3h-h=5$

$⟹2h=5$

$\therefore h=\frac{5}{2}=2.5m$

From, $\left(i\right)⟹x=\sqrt{3}\left(2.5\right)=1.732\times 2.5=4.33m$

i.e., The height of the tower $h=2.5m$

the distance of the point from the tower $x=4.33m$