Answer
$$c^{2} =a^{2}-2 a b \cos \theta+b^{2}$$
Work Step by Step
From the given figure, we apply the Pythagorean Theorem:
\begin{aligned}
\text {Hypotenuse}^{2}&=\operatorname{side}^{2}+\text { side }^{2}\\
c^{2}&=(a-b \cos \theta)^{2}+(b \sin \theta)^{2}\\
c^{2}&=a^{2}-2(a)(b \cos \theta)+b^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta\\
c^{2}&=a^{2}-2 a b \cos \theta+b^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta\\
c^{2}&=a^{2}-2 a b \cos \theta+b^{2}
\end{aligned}
