# 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?

##### 1 Answer

Feb 5, 2016

#### Answer:

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

# color(blue)(" Cosine Rule ") color(black)(" stated below ") # for this triangle :

# C^2 = A^2 + B^2 - ( 2AB costheta) # where

#theta color(black)(" is angle between A and B") # here A = 2 , B = 3 and

#theta =( 5pi)/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#