Question

Two pillars of equal height stand on either side of a roadway that is $60m$ wide. At a point in the roadway between the pillars, the elevation of the top of the pillars is $60°$ and$30°$. The height of the pillars is

• A. $15\sqrt{3}m$
• B. $\frac{15}{\sqrt{3}}m$
• C. $15m$
• D. $20m$

Answer 1

The correct option is A

$15\sqrt{3}m$

The explanation for the correct answer.

Solve for the height of pillars.

$AB$ and$CD$ are the two pillars.

$BD=60m$

$\angle APB={60}^{\circ }$ and $\angle CPD={30}^{\circ }$

In triangle$ABP$,$\tan {60}^{\circ }=\frac{AB}{BP}$

$BP=\frac{h}{\tan \left({60}^{\circ }\right)}=\frac{h}{\sqrt{3}}$

In triangle $CDP,\frac{CD}{DP}=\tan {30}^{\circ }$

$PD=\sqrt{3}h$

$60=BP+PD$

$60=\sqrt{3}h+\left[\frac{h}{\sqrt{3}}\right]$

$h=\frac{60}{\sqrt{3}+\left({\displaystyle \frac{1}{\sqrt{3}}}\right)}$

$=15\sqrt{3}m$

Hence, option(A) is the correct answer.