根据正弦定律得知
a/sinA=b/sinB=c/sinC=k
b-c=2acos(60°+C)
ksinB-ksinC=2ksinAcos(60°+C)
sinB-sinC=2sinAcos(60°+C)
sin(A+C)-sinC=sinA(cosC-√3sinC)
sinAcosC+cosAsinC-sinC=sinAcosC-√3sinAsinC
cosAsinC+√3sinAsinC-sinC=0
cosA+√3sinA=1
2sin(30°+A)=1
sin(30°+A)=1/2
30°+A=150 °
A=120°