Question

If two sides of a triangle are “a” units & 10 units and the angles opposite of them are 30°and 60° 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 (A) = Sin(30°) = 1 /2

Sin (B) = Sin (60°) = $\frac{\sqrt{3}}{2}$
$\frac{a}{1/2}=\frac{10}{\sqrt{3}/2}$
$a=\frac{10}{\sqrt{3}}$