Question

A vertical tower stands on a horizontal plane is surmounted by a vertical flagstaff. At a point on the plane $70$ meters away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively ${60}^o$ and ${45}^o$. Find the height of the flagstaff and that of the tower.

Answer 1

Given that the distance of the observer from the Tower $=x=70m$

Now, Let the Height of the Tower be $q$

and Height of Flagstaff be $p$

From $△ABC$

$\tan {60}^o=\frac{p+q}{70}\Rightarrow p+q=70\sqrt{3}..........\left(1\right)$

and

From $△DBC$

$\tan {45}^o=\frac{q}{70}\Rightarrow q=\mathrm{70................}\left(2\right)$

From (1) and (2)

$p+70=70\sqrt{3}$

$\Rightarrow p=70(\sqrt{3}-1)=51.24m$ $(Take\sqrt{3}=1.73)$

Therefore, Height of Tower $=70m$

and Height of Flagstaff $=51.24m$