Question

A triangle has sides A, B, and C. Sides A and B are of lengths `8` and `1`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

`C=8.4334`

Explanation:

We have two lengths and the angle between them. As such, to determine length C (the opposite length) we must use the law of cosines, in our case that will be:

`C^2=A^2+B^2-2ABcos(x)`

where `x` is the angle made between `A` and `B`.

Plugging in the numbers gives us:

`C^2=8^2+1^2-2(8)(1)cos((5 pi)/8)`

`=65-16(-0.382683)`

`=65+6.12293=71.1229`

So:

`C^2=71.1229`

`therefore C = sqrt(71.1229)=8.4334`