Question

given problem type SAA or ASA, how would you solve for the length of any of the remaining sides?

Answer 1

This is the concept of geometry and trigonometry, when you have been givn a problem type SAA (side-angle-angle) or ASA (Angle-side-angle), to solve the problem of this kind we use the sine rule which states that given triangle ABC with sides a,b,c. Then;
a/sin A=b/sin B=c/sin C

Answer 2

Use the fact that the angles add up to 180 degrees, and then use the law of sines.