# 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?

##### 1 Answer

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

#color(blue)(" cosine rule ")# for this triangle the cosine rule is

# C^2 = A^2 + B^2 - (2ABcostheta)# here A = 3 , B = 2 and

#theta = (5pi)/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#