# A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #5#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

##### 1 Answer

Feb 5, 2016

C ≈ 3.66

#### Explanation:

Given a triangle with 2 sides and the angle between them known ,use the

#color(blue)(" cosine rule ")color(black)(" to solve for C")# In relation to this triangle the cosine rule is :

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

#theta color(black)(" is the angle between A and B")# here A = 7 , B = 5 and

#theta = pi/6 #

#rArr C^2 = 7^2 + 5^2 - [ 2 xx 7 xx 5 xx cos(pi/6)] # = 49 + 25 - ( 60.6217..) ≈ 13,38

( remember this is

#C^2 # )

#rArr C = sqrt13.38 ≈ 3.66#