在三角形ABC中,角A、B、C所对的边分别为a、b、c若sin^B+sin^C=sin^A+sinBsinC,且向量AC

(sinB)^2+(sinC)^2=(sinA)^2+(sinBsinC)
a/sinA=b/sinB=c/sinC=1/k
(bk)^2+(ck)^2=(ak)^2+bck^2
b^2+c^2=a^2+bc
cosA=(b^2+c^2-a^2)/2bc=1/2
sinA=√3/2
AC*AB=|AC|*|AB|cosA=4
|AC|*|AB|=8
S=|AC|*|AB|sinA /2=2√3