由题意sin^2(A/2)=(c-b)/2c
即 2sin^2(A/2)=(c-b)/c =1-b/c
1-2sin^2(A/2)=b/c
cosA=b/c=sinB/sinC sinB=sinCcosA sinB= sin(A+C)=sinAcosC+cosAsinC 所以sinAcosC=0 cosC=0 C是直角!即三角形ABC为直角三角形.