# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 2, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Apr 5, 2017

#### Answer:

The length of side $C$ is $9.17 \left(2 \mathrm{dp}\right)$

#### Explanation:

Given $A = 8 , B = 2 , \angle c = \frac{2 \cdot \pi}{3} = \frac{2 \cdot 180}{3} = 120$

Applying cosine law we get $C = \sqrt{{A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos c} \mathmr{and} C = \sqrt{64 + 4 - 32 \cdot \cos 120} = \sqrt{68 - 32 \cdot \left(- 0.5\right)} = \sqrt{68 + 16} = \sqrt{84} \approx 9.17 \left(2 \mathrm{dp}\right)$ unit [Ans]