How do you use sine and cosine to find the hypotenuse length of a triangle?

All the trig functions are equations of 3 variables. If you have 2 of the variables you can calculate the third. The only slight complication in your case is that you don't have the trig function itself but you have the angle and you have to look up the function. The function and the side length make up 2 of the variables for either the sine or cosine function and you can calculate the hypotenuse from them.