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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Proving that larger side corresponds to larger angle

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