acosC+√3 asinC-b-c=0
acosC+√3 asinC=b+c
由正弦定理,得
sinAcosC+√3 sinAsinC
=sinB+sinC
=sin（A+C）+sinC
=sinAcosC+sinCcosA+sinC
即,√3 sinAsinC =sinCcosA+sinC
因为sinC≠0
所以,√3 sinA-cosA=1
sin（A-30°）=1/2
A=60°如果A=150°sin（A-30°）=sin（120°）=√3/2而题目中sin（A-30°）=1/2