由sin^2A+sin^2B-sinAsinB=sin^2C
由正弦定理sinA=a/2R,sinB=b/2R,sinC=c/2R
则(a/2R)^2+(b/2R)^2-(a/2R)(b/2R)=(c/2R)^2
可得c^2=a^2+b^2-ab
由余弦定理c^2=a^2+b^2-2abcosC
所以cosC=1/2,sinC=√3/2
S△ABC=1/2*absinC=1/2*4*√3/2=√3