A 是锐角
设tanA=m (m>0)
tanB=2m
tanC=tan[π-(A+B)]
=-tan(A+B)
=-(m+2m)/(1-2m²)=3m
所以 1-2m²=-1
m=1
所以 tanA=1,tanB=2,tanC=3
sinA=√2/2,sinB=2/√5,sinC=3/√10
AC/AB=sinB/sinC=(2/√5)/(3/√10)=(2/√5)*√10/3=2√2/3