if two sides between the contained angle are 15 and 30 where the contained angle is 20, is the length of the other side 16.7 or 14.5?
16.7
Use the cosine rule. Let A denote the contained angle, a denotes side opposite angle A, and b and c are the remaining two sides.
$\displaystyle a^2 = b^2 + c^2 - 2bc\cos{A}$
$\displaystyle a^2 = 1125 - 900\cos{20}$
$\displaystyle a = \sqrt{1125 - 900\cos{20}} \approx 16.71157208$