# A triangle has sides A, B, and C. Sides A and B are of lengths 3 and 2, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Feb 13, 2016

C ≈ 3.15

#### Explanation:

In this triangle , 2 sides and the angle between them are known.In this situation to solve for C use $\textcolor{b l u e}{\text{ cosine rule }}$

for this triangle the cosine rule is

${C}^{2} = {A}^{2} + {B}^{2} - \left(2 A B \cos \theta\right)$

here A = 3 , B = 2 and $\theta = \frac{5 \pi}{12}$
substitute these values into formula

 C^2 = 3^2 + 2^2 - ( 2 xx 3 xx2cos((5pi)/12 )

= 9+4 - 3.1 = 13 - 3.1 = 9.9

 C^2 = 9.9 rArr C = sqrt9.9 ≈ 3.15