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 `pi/6`. What is the length of side C?

Answer 1

Length of `C ~~2.72`

Explanation:

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

So for the given values:
`color(white)("XXX")C^2=3^2+1^2-3cos(pi/6)`
`color(white)("XXX")=10-(3sqrt(3))/2`
`color(white)("XXX")~~7.401924`

`C~~sqrt(7.401924)~~2.72`