a^2+b^2+c^2=4√3S c^2=a^2+b^2-2ab·cosC S=1/2absinC
代入化简,a^2+b^2=2ab(√3/2sinC+1/2cosC)=2ab·cos(60°-C)
cos(60°-C)=(a^2+b^2)/2ab≥1,显然cos(60°-C)=1（当且仅当a=b）
C=60°