Question

Two lamp posts are of equal height. A boy standing mid-way between then observes the elevation of the top of either post to be ${30}^{\circ }$. After walking $15m$ towards one of them, he observes the elevation of it stop to be ${60}^{\circ }$. Find the heights of the posts and the distance between them.

• A. 45 m
• B. 55 m
• C. 48 m
• D. 63 m

Answer 1

The correct option is A

45 m

Let us draw a figure with given information as follows:

From right angled triangle $\Delta ABC$, we have
$\tan {60}^{\circ }=\frac{y}{x}$
$\Rightarrow \sqrt{3}=\frac{y}{x}$
$\Rightarrow y=\sqrt{3}x$.....(i)

Similar way, from right angled triangle $\Delta ABD$
$\tan {30}^{\circ }=\frac{y}{x+15}$
$\frac{1}{\sqrt{3}}=\frac{y}{x+15}$
$x+15=\sqrt{3}y$
$\Rightarrow x+15=\sqrt{3}\left(\sqrt{3}x\right)$
$\Rightarrow x+15=3x$
$\Rightarrow 3x-x=15$
$\Rightarrow 2x=15$
$\therefore x=7.5m$
Hence, $y=\sqrt{3}\times 7.5$
$\therefore y=12.975m$
$BD=x+15=7.5+15=22.5m$
Since, $D$ is mid point of $BE$.
So, $BE=2BD$
$=2\left(22.5\right)$
$\therefore BE=45m$
Hence, the distance between the poles $=45m$