Question

A flagstaff $10m$ high stands at the center of a equilateral triangle which is horizontal at the top of the flagstaff. Each side subtends at an angle of ${60}^o$. The length of each side of the triangle is:

• A. $\frac{6\sqrt{3}}{3}$
• B. $\frac{4\sqrt{6}}{3}$
• C. $\frac{20}{\sqrt{3}}$
• D. $\frac{6\sqrt{5}}{3}$

Answer 1

Answer: (C)

$\frac{20}{\sqrt{3}}$

$\Rightarrow$ Considering Right angle $△ADC$ we have,

$\Rightarrow$ $\tan {60}^o=\frac{AD}{DC}$

$\Rightarrow$ $\sqrt{3}=\frac{10}{DC}$

$\Rightarrow$ $DC=\frac{10}{\sqrt{3}}$

$\Rightarrow$ $DC=\frac{10}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$\therefore$ $DC=\frac{10\sqrt{3}}{3}$

$\Rightarrow$ $BC=2\times DC$

$\therefore$ $BC=2\times \frac{10\sqrt{3}}{3}$

$\therefore$ $BC=\frac{20\sqrt{3}}{3}$

$\therefore$ The length of each side of the triangle is $\frac{20}{\sqrt{3}}m$