Question

If two sides of a triangle are "a" units & 10 units and the angles opposite of them are ${30}^{\circ }$ and ${60}^{\circ }$ respectively then find the value of a.

• A. 5
• B. 10
• C. $\frac{10}{\sqrt{3}}$
• D. $10\sqrt{3}$

Answer 1

The correct option is C $\frac{10}{\sqrt{3}}$

We are given two angles and one side, so we'll apply sine rule to calculate the other side. According to sine rule -
$\frac{a}{sin\left(A\right)}=\frac{b}{sin\left(B\right)}$
Here, b = 10
$sin\left(A\right)=sin\left({30}^{\circ }\right)=\frac{1}{2}$
$sin\left(B\right)=sin\left({60}^{\circ }\right)=\frac{\sqrt{3}}{2}$
$\frac{a}{\frac{1}{2}}=\frac{10}{\frac{\sqrt{3}}{2}}$
$a=\frac{10}{\sqrt{3}}$