在三角形ABC中,内角A,B,C的对边的边长分别是a,b,c,已知c=2,角C=π/3 若三角形的面积等于根号3 求a ,b .

三角形的面积 = 1/2 ab sinC = 1/2ab 根号3 / 2 = 根号3
ab = 4
cos C = (a^2+b^2-c^2) / (2ab) = 1/2
a^2+b^2 = 8
a = 2,b = 2
sin B = 2 sin A
a / sinA = b / sin B
a = b/2
cos C = (a^2+b^2-c^2) / (2ab) = 1/2
a= 2根号3 / 3
b = 4根号3 / 3
三角形ABC的面积 = 1/2 ab sinC = 2根号3 / 3