设三个角比为A:B:C = x:y:z.
则,A = xt,B = yt,C = zt,
其中,t为待定常数.
因PI = A + B + C = t(x+y+z),
t = PI/(x+y+z).
A = xPI/(x+y+z),
B = yPI/(x+y+z),
C = zPI/(x+y+z).
再利用正弦定理,
a:b:c = sin(A):sin(B):sin(C) = sin[xPI/(x+y+z)] :sin[yPI/(x+y+z)] :sin[zPI/(x+y+z)]