# 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)/8 #. What is the length of side C?

##### 1 Answer

Sep 29, 2016

#### Answer:

#### Explanation:

Given a triangle, where 2 sides and the angle between them are known, in this case A and B and we wish to calculate the length of the third side C, use the

#color(blue)"cosine rule"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(C^2=A^2+B^2-(2ABcos("angle between them")))color(white)(a/a)|)))# here A = 7 , B = 5 and angle between them

#=pi/8# substitute these values into the 'cosine rule'

#C^2=7^2+5^5-(2xx7xx5xxcos(pi/8))#

#=49+25-(64.672...)#

#=74-(64.672...)≈9.328# Now

# C^2≈9.328rArrC=sqrt(9.328)≈3.054#