Question

A triangle has sides A, B, and C. Sides A and B are of lengths `1` and `6`, respectively, and the angle between A and B is `(5pi)/6`. What is the length of side C?

Answer 1

`c=sqrt(37+6sqrt(3))`

Explanation:

We use the Theorem of cosines:

`c^2=a^2+b^2-2abcos(gamma)`
and that
`cos(5/6*pi)=-sqrt(3)/2`
since
`b=1,a=6`

we get

`c^2=1+36-2*6*(-sqrt(3)/2)`
this is
`c=sqrt(37+6*sqrt(3))`