因a+c=2b,故由正弦定理有：sinA+sinC=2sinB
sinA+sinC=2[sin(A+C)/2]cos(A-C)/2=
=2[sin(180-B)/2]*cos30(度）
=2sin(90-B/2)*根号3/2
=(根号3)cosB/2
故,2sinB=(根号3)cosB/2
2*2sinB/2*cosB/2=(根号3)cosB/2,因cosB/20
故sinB/2=(根号3)/4
又,sinB/2=±根号[(1-cosB)/2]
cosB=1-2sin^2(B/2)=1-2*3/16=5/8
故,sinB=根号(1-cos^2)=根号[1-(5/8)^2]=(根号39)/8