A triangle has sides A, B, and C. Sides A and B are of lengths 99 and 77, respectively, and the angle between A and B is (7pi)/8 7π8. What is the length of side C?

2 Answers
Nov 6, 2016

"C"=15.7C=15.7

Explanation:

To answer this question, we have to use the law of cosines.

"C"^2="A"^2+"B"^2-2"AB"cos("c")=81+49-126cos(7/8pi) =246.4C2=A2+B22ABcos(c)=81+49126cos(78π)=246.4

"C"=sqrt264.4=15.7C=264.4=15.7

Nov 6, 2016

2.0359.....

Explanation:

Cosine rule (rearranged for c) = c^2 = a^2+b^2-2ab*cosCc2=a2+b22abcosC

=c= sqrt(9^2+7^2-2*9*7*cos( (7pi)/8))=c=92+72297cos(7π8)

=2.035924013