Question

A triangle has sides A, B, and C. Sides A and B are of lengths `5` and `3`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

`c=sqrt(34-15sqrt(2-sqrt(3))`

Explanation:

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

`c^2=9+25-30*(sqrt(3)-1)/(2sqrt(2))`
or

`c=sqrt(34-15sqrt(2-sqrt(3))`