设三边长a,b,c则CA*(AB-AC)=CA*CB=bacosC=18
sinC=√3/2,cosC=1/2所以ab=36
c²=a²+b²-2abcosC=a²+b²-36即a²+b²=c²+36
sinA+sinB=2sinC,a+b=2c平方得a²+b²+2ab=4c²
c²+36+72=4c²,得c=6,|AB|=6
设三边长a,b,c则CA*(AB-AC)=CA*CB=bacosC=18
sinC=√3/2,cosC=1/2所以ab=36
c²=a²+b²-2abcosC=a²+b²-36即a²+b²=c²+36
sinA+sinB=2sinC,a+b=2c平方得a²+b²+2ab=4c²
c²+36+72=4c²,得c=6,|AB|=6