Question

已知在三角形ABC中,acosC+根号3倍的asinC-b-c=0.求∠A

Answer 1

边化角得：sinAcosC＋√3sinAsinC－sinB－sinC=0 sinAcosC＋√3sinAsinC－sin(A＋C)－sinC=0 sinAcosC＋√3sinAsinC－sinAcosC－cosAsinC－sinC=0 √3sinAsinC－cosAsinC－sinC=0√3sinA=1＋cosA

用配角公式得sin(A+30)=1

所以A+30=90

A=60