How do you find the hypotenuse of a right triangle when only a side length and angle is given?

Dependent on what side you are given you would use Sin(Θ) = Opposite/Hypotenuse just rearrange the formula to Hypotenuse = Opposite/Sin(Θ).

Or if you are given the adjacent side use Cosine(Θ)=Adjacent/Hypotenuse, then:

Hypotenuse = Adjacent/Cosine(Θ)