cosA=√6/3
那么A为锐角
sinA=1/√3
sin(π/2+B)=2√2/3
cosB=2√2/3
B为锐角
sinB=1/3
sinC=sin(180-A-B)=sin(A+B)=sinAcosB+cosAsinB=1/√3*2√2/3+√6/3*1/3=√6/3
正弦定理
b/sinB=c/sinC
b/(1/3)=2√2/(√6/3)
b=2√3/3
S=1/2bcsinA=1/2×2√3/3×2√2×1/√3=2√2/3