sinAsinB=3/4 (a^3+b^3-c^3)/(a+b-c)=c^2

(a^3+b^3-c^3)/(a+b-c)=c^2
a^3+b^3-c^3=ac^2+bc^2-c^3
a^3+b^3=c^2(a+b)
(a+b)(a^2-ab+b^2)=c^2(a+b)
a^2+b^2-ab=c^2

由余弦定理a^2+b^2-c^2=2abcosC得：
a^2+b^2＝c^2+2abcosC
∵a^2+b^2=c^2+ab
∴cosC=1/2
∴C＝60°
∴A+B=2π/3.
sinAsinB=sinAsin[(2π/3)-A]
=sinA(sin2π/3cosA-cos2π/3sinA)
=根号3/4sin2A+1/4-1/4cos2A=3/4
∴sin(2A-π/6)=1.
又∵-π/6<2A-π/6<11π/6,
∴2A-π/6=π/2,
A=π/3.
∴三角形为正三角形,即锐角三角形