a^2=b^2+c^2-2bccosA; 2abccosA=a(b^2+c^2-a^2);
b^2=a^2+c^2-2accosB; 2abccosB=b(a^2+c^2-b^2);
c^2=a^2+b^2-2abcosC; 2abccosC=c(a^2+b^2-c^2).
Add these together:
a^2+b^2+c^2=2(a^2+b^2+c^2)-2(bccosA+accosB+abcosC);
2(bccosA+accosB+abcosC)=a^2+b^2+c^2.
sinA/a=sinB/b=sinC/c; sinA=asinB/b=asinC/c; sinB=bsinA/a=bsinC/c; sinC=csinA/a=csinB/b.
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