# If in an equilateral triangle R=3^(1/2) cm Then the length of each side of the triangle is?

Oct 22, 2017

$3 \text{cm.}$

#### Explanation:

From Trigonometry, we know that, in $\Delta A B C ,$

$\text{Sine-Rule : } \frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{\sin} C = 2 R .$

Since $\Delta A B C$ is equilateral, we have,

$a = b = c , \mathmr{and} , A = B = C = \frac{\pi}{3.}$

Hence, $a = b = c = 2 R \sin A = 2 \cdot \sqrt{3} \cdot \sin \left(\frac{\pi}{3}\right) = 2 \sqrt{3} \cdot \frac{\sqrt{3}}{2.}$

$\Rightarrow \text{ the length of each side is "3"cm.}$