Question

Two poles standing on a horizontal ground are of heights $5$ m and $10$ m respectively. The line joining their tops makes an angle of ${15}^{\circ }$ with ground. Then the distance (in m) between the poles, is :

• A. $\frac{5}{2}(2+\sqrt{3})$
• B. $10(\sqrt{3}-1)$
• C. $5(2+\sqrt{3})$
• D. $5(\sqrt{3}+1)$

Answer 1

The correct option is C $5(2+\sqrt{3})$


Let $AB$ and $CD$ be the two poles.
Distance between them is $X$ units.
$AE=5$
$\tan {15}^{\circ }=\frac{AE}{EC}=\frac{5}{X}$
$\Rightarrow 2-\sqrt{3}=\frac{5}{X}$
$\Rightarrow X=\frac{5}{2-\sqrt{3}}$
On rationalizing, we have
$X=5(2+\sqrt{3})$ m