# A triangle has sides A, B, and C. Sides A and B are of lengths 6 and 2, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Mar 25, 2016

≈ 7.211 units

#### Explanation:

Given a triangle , where 2 sides and the angle between them are known, we can use the$\textcolor{b l u e}{\text{ cosine rule " " to find C }}$

${c}^{2} = {a}^{2} + {b}^{2} - \left(2 a b \cos \theta\right)$

where a and b are the 2 known sides and $\theta \text{ the angle between them }$

here a = 6 , b = 2 and $\theta = \frac{2 \pi}{3}$

substitute these values into the equation

$\Rightarrow {c}^{2} = {6}^{2} + {2}^{2} - \left[2 \times 6 \times 2 \times \cos \left(\frac{2 \pi}{3}\right)\right]$

= 36 + 4 - (-12) = 52

now  c^2 = 52 rArr c = sqrt52 ≈ 7.211