#### Answer

The length of side $c$ is approximately $1.951$

#### Work Step by Step

$$a = 2 \hspace{1cm}b=3\hspace{1cm}C=40^\circ$$
- Recall the law of cosines: $$c^2=a^2+b^2-2ab\cos C$$
Therefore, we can calculate the length of side $c$:
$$c^2=2^2+3^2-2\times2\times3\times\cos40^\circ$$
- Here there is no exact value of $\cos40^\circ$, so we would take an approximate value from calculator, which I would take $\cos40^\circ\approx0.766$
$$c^2=4+9-12\times0.766$$
$$c^2=13-9.192$$
$$c^2=3.808$$
$$c\approx1.951$$ (because the length of a side of a triangle is positive)