Question

A triangle has sides A, B, and C. Sides A and B are of lengths `10` and `12`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

`C=18.33`

Explanation:

As per law of cosines
`C^2=A^2+B^2-2Atimes Btimescos(theta)` where `A=10;B=12 and theta=(5pi)/8`
or
`C^2=10^2+12^2-2times10times12timescos((5pi)/8)`
or
`C^2=100+144-240times(-0.383)`
or
`C^2=100+144+91.84`
or
`C^2=335.84`
or
`C=sqrt335.84`
or
`C=18.33`