Question

A triangle has sides A, B, and C. Sides A and B are of lengths `3` and `1`, respectively, and the angle between A and B is `(7pi)/12`. What is the length of side C?

Answer 1

approximately (to 3 decimal places): `3.400`

Explanation:

The Law of Cosines tells us:
`color(white)("XXX")C^2=A^2+B^2-2ABcos(/_c)`
where `/_c` is the angle between `A` and `B` (i.e. the angle opposite side `C`)

`C^2=3^2+1^1-2 * 3 * 1 * cos((7pi)/12)`

`color(white)("XXX")=9+1- 6 * (-0.252914271)color(white)("xxx")`(calculator use for this and all points beyond)

`color(white)("XXX")=10+1.55291427`

`color(white)("XXX")=11.55291427`

`C=sqrt(11.55291427)`

`color(white)("XX")=3.398957821`