AB=2BC
AB/sinC=BC/sinA
2BC/sinC=BC/sinA
sinC=2sinA
∵B=60
∴C+A=120
∴C=120-A
∴sinC=sin(120-A)=sin120cosA-cos120sinA=2sinA
√3/2 cosA+sinA/2=2sinA
√3/2 cosA=3/2sinA
√3cosA=3sinA
cosA=√3sinA 平方一下
cos^2A=1-sin^2A=3sin^2A
4sin^2A=1
∵A0
sinA=1/2
A=30
C=120-A=90
∴三角形ABC是直角三角形