Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height $5$ meters. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are respectively ${30}^o$ and ${60}^o$. Find the height of the tower.

Answer 1

Given that the Height of Flagstaff $=5m$
Now, Let the Height of the Tower be $q$
and distance of a point from the Tower be $x$
From $△ABC$
$\tan {60}^o=\frac{5+q}{x}\Rightarrow 5+q=x\sqrt{3}..........\left(1\right)$
and
From $△DBC$
$\tan {30}^o=\frac{q}{x}\Rightarrow x=q\sqrt{3}................\left(2\right)$

From (1) and (2)

$5+q=\sqrt{3}\times q\sqrt{3}$

$\Rightarrow 5+q=3q$

$\Rightarrow 2q=5\Rightarrow q=2.5$

Therefore, Height of Tower $=2.5m$