Question

A triangle has sides A, B, and C. Sides A and B are of lengths `8` and `4`, respectively, and the angle between A and B is `(11pi)/12`. What is the length of side C?

Answer 1

`C ~= 11.9`

Explanation:

If we denote the angle between `A` and `B` as `/_C` (not to be confused with the side `C` opposite `/_C`)

The Law of Cosines tells us
`color(white)("XXX")C^2 = A^2+B^2 - 2AB*cos(/_C)`
`rArr`
`color(white)("XXX")C = sqrt(A^2+B^2 - 2AB*cos(/_C))`

We are told that
`color(white)("XXX")A=8`
`color(white)("XXX")B=4`
`color(white)("XXX")/_C = (11pi)/12`

Plugging these values into the formula gives
`color(white)("XXX")C=11.90878889`