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

Feb 5, 2016

C ≈ 3.15

#### Explanation:

In this question since 2 sides A and B of the triangle are known as is the angle between them then use

$\textcolor{b l u e}{\text{ Cosine Rule ") color(black)(" stated below }}$

for this triangle :

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

where $\theta \textcolor{b l a c k}{\text{ is angle between A and B}}$

here A = 2 , B = 3 and $\theta = \frac{5 \pi}{12}$

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

 rArr C^2 = 4+9 - (12 xx cos((5pi)/12) ≈9.9

( remember this is C^2 )

 rArr C = sqrt9.9 ≈ 3.15