Question

At a distance $2h$ $m$ from the foot of a tower of height $h$ $m$, the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

• A. $\frac{5h}{3}m$
• B. $\frac{4h}{3}m$
• C. $\frac{7h}{5}m$
• D. $\frac{3h}{2}m$

Answer 1

The correct option is A $\frac{5h}{3}m$

In $\Delta ABD$, $\tan \alpha =\frac{h}{2h}$
$\Rightarrow \tan \alpha =\frac{1}{2}$
In $\Delta ABC$,
$\tan 2\alpha =\frac{h+p}{2h}$
$\Rightarrow \frac{2\tan \alpha }{1-{\tan }^2\alpha }=\frac{h+p}{2h}$
$\Rightarrow \frac{2\left(\frac{1}{2}\right)}{1-{\left(\frac{1}{2}\right)}^2}=\frac{h+p}{2h}$
$\Rightarrow \frac{4}{3}=\frac{h+p}{2h}$
$\Rightarrow 8h=3h+3p$
$\Rightarrow 5h=3p\Rightarrow p=\frac{5h}{3}m$