根据正弦定理得,sinC/sinB=AB/AC=2(√6+1)/5
2(√6+1)AC=5AB
∵AB=2
∴AC=5/（√6+1）=√6-1
又根据余弦定理
cosA=(AC²+AB²-BC²)/(2*AC*AB)=（2-2√6）/[4(√6-1)]
=-1/2
A=120°