在三角形ABC中,角A,B,C所对的边分别为a,b,c,若sin^2B+sin^2C=sin^2A+sinBsinC,且向量AC*向量AB=4

正弦定理：a/sinA=b/sinB=c/sinC∴b^2+c^2=a^2+bca^2=b^2+c^2-bc又余弦定理:a^2=b^2+c^2-2bccosA∴cosA=1/2,A=π/3,sinA=√3/2AC*AB=|AC| |AB| cosA=4 (AC、AB均为向量) |AC| |AB|=8S=|AB| |AC|sinA/2=2√3...