Question

A triangle has sides A, B, and C. Sides A and B are of lengths `4` and `2`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

`C~=4`

Explanation:

As per law of cosines
`C^2=A^2+B^2-2Atimes Btimescos(theta)` where `A=4;B=2 and theta=(5pi)/12`
or
`C^2=4^2+2^2-2times4times2timescos((5pi)/12)`
or
`C^2=16+4-16times(0.2588)`
or
`C^2=20-4.14`
or
`C^2=15.86`
or
`C=sqrt15.86`
or
`C~=4`