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

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

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