Question

A triangle has sides A, B, and C. Sides A and B are of lengths `8` and `7`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

`sqrt(113-28*sqrt(2)*(sqrt(3)-1))`

Explanation:

Using the Theorem of cosines:

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

`cos(5*pi/12)=(sqrt(3)-1)/(2sqrt(2))`
we get

`c=sqrt(113-28*sqrt(2)(sqrt(3)-1))`