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 `pi/3`. What is the length of side C?

Answer 1

`C=sqrt57`

Explanation:

By the Carnot theorem, you know that:

`C^2=A^2+B^2-2ABcosgamma`

Since `A=8, B=1 and gamma=pi/3`:

`C=sqrt(8^2+1^2-2*8*1*cos(pi/3))`

`C=sqrt(65-16*1/2)`

`C=sqrt57`