I was asked by one of my professors to prove for the class why the largest side of the tringle corresponds to the largest angle of that triangle. I was thinking of using law of sines to do so. Please let me know if I am wrong so that I do not look like a fool in front of class. My triangle is ABC with vertices/angles a,b, and c respectively. I am saying that angle a is the largest in that triangle, so; Quick notes: L is my representation for angle. mLa > mLb > mLc. Law of Sines: sin(a)/BC = sin(b)/AC = sin(c)/AB therefore; AC*sin(a)=BC*sin(b), AC*sin(c)=AB*sin(b), AB*sin(a)=BC*sin(c). so; AC/BC = sin(b)/sin(a), AC/AB = sin(b)/sin(c), AB/BC = sin(c)/sin(a). once again; mLa > mLb > mLc. therefore; sin(a) > sin(b) > sin(c) so if; AC/BC = sin(b)/sin(a), AC/AB = sin(b)/sin(c), AB/BC = sin(c)/sin(a). then; AC < BC AC > AB AB < BC so; BC > AC > AB I don't know if I need to write anything more down from here. Take it easy on my, I threw this together last night while ignoring my mother-in-law's boring story.