A triangle $ABC$ is drawn with angle $A={46}^{\circ }.$

The side $AC$ has length $\sqrt{85}$ and the side $BC$ has length $2\sqrt{13}.$

1. Find, to three significant figures, the two possible lengths of side $c.$

2. Sketch the triangle in each case.

You should use the cosine rule in the form

When you use the cosine rule, you should end up with a quadratic in terms of $c$.

You will need the quadratic formula (or completing the square).