Question

Two poles of equal heights are standing opposite each other on either side of the road which is $80$ m wide. From the points between them on the road, the elevation of the top of the poles are ${60}^{\circ }$ and ${30}^{\circ }$ respectively. Find the height of the poles.

• A. $10\sqrt{3}$ m
• B. $20\sqrt{3}$ m
• C. $20$ m
• D. $15\sqrt{3}$ m

Answer 1

The correct option is B $20\sqrt{3}$ m

In $\Delta DPC$

$\tan p=\frac{CD}{CP}$

$\tan {30}^0$

$\frac{1}{\sqrt{3}}=\frac{CD}{CP}$

$CP=\frac{CP}{\sqrt{3}}$ (1)

IN $\Delta APB$

$\tan p=\frac{AB}{PB}$

$\tan {60}^0=\frac{AB}{BP}$

$\sqrt{3}BP=AB$

$CD=\sqrt{3}BP$ (2)

FROM (1) & (2)

$\frac{CP}{\sqrt{3}}=\sqrt{3}BP$

$CP=3BP$

NOW ,$BC=BP+CP$

$80=BP+3BP$

$BP=20m$

$CP=60m$

$CD=\sqrt{3}BP$

$=20\sqrt{3}$