设ΔABC三点分别为(a1,a2)(b,0)(0,0),sinB=a2/(a1^2+a2^2)^0.5,sinC=a1/((a1-b)^2+a2^2)^0.5.这里设(a1^2+a2^2)^0.5为x,设((a1-b)^2+a2^2)^0.5为y.(我写得累死了).sinA=sin(B+C)=sinBcosC+sinCcosB =a2a1/xy+a2(b-a1)/xy=a2b/xy,sinA/BC=a2/xy,sinB/AC=a2/xy,sinC/AB=a2/xy.
证毕.