由正弦定理出发,我们可以得到如下定理:定理:△ABC中,以sinA,sinB,sinC为边可构成三角形A’B’C’且△ABC∽△A’B’C’,△A’B’C’外接圆直径为l。证明:sinA+sinB=1/2R(a+b)>c/2R=sinC,同理sinA+sinC>sinA,sinC+sinA>sinB。因此由sinA,sinB,sinC可构成三角形。由正弦定理a/sinA=b/sinB=c/sinC=2R,得出 Starting from the sine theorem, we can obtain the following theorem: Theorem: △ABC, with sinA, sinB, sinC for the edge can constitute the triangle A’B’C’ and △ABC ∽ △ A’B’C’, △ A’B The diameter of the ’C’ circumcircle is l. Proof: sinA+sinB=1/2R(a+b)>c/2R=sinC, similarly sinA+sinC>sinA, sinC+sinA>sinB. Therefore, sinA, sinB, and sinC can form triangles. Derived from the sine theorem a/sinA=b/sinB=c/sinC=2R