(1)a/sina=b/sinb=c/sinc=2r(r外接圆半径),
sina=a/2r sinb=b/2r sinc=c/2r .
sinA^2+sinB^2-sinC^2=sinA*sinB
a^2/4r^2+b^2/4r^2-c^2/4r^2=ab/4r^2
得a^2+b^2-c^2=ab
由余弦定理:cosc=(a^2+b^2-c^2)/2ab 得cosc=1/2
∴c=60°
(2)sinc=√3/2=c/2r=c/4
∴c=2√3,
s△=(1/2)absinc=√3
∴ab=4
由a^2+b^2-c^2=ab 变形(a+b)^2-3ab-c^2=0
(a+b)^2-12-12=0
a+b=√24