Question

A triangle has sides A, B, and C. Sides A and B are of lengths `6` and `8`, respectively, and the angle between A and B is `(7pi)/8`. What is the length of side C?

Answer 1

`c=sqrt(100-48sqrt(2+sqrt(2))`

Explanation:

Note that

`cos(pi/8)=-1/2*sqrt(2+sqrt(2))`
so we get after the Theorem of cosines

`c^2=a^2+b^2-2abcos(gamma)`

`c=sqrt(36+64-96*cos(pi/8))`
and we get

`c=sqrt(100-48sqrt(2+sqrt(2)))`