# A triangle has sides A, B, and C. Sides A and B are of lengths 10 and 12, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Apr 30, 2018

c=19.07878403

#### Explanation:

Cosine rule ${c}^{2} = {a}^{2} + {b}^{2} - 2 b c$CosA

${c}^{2} = {10}^{2} + {12}^{2} - \left\{2 \times 10 \times 12 \times C o s \left(\frac{2}{3} \pi\right)\right\}$

${c}^{2} = 244 - \left\{- 120\right\}$

$c = \sqrt{364}$

c=19.07878403