根据正弦定理得
b/sinB=c/sinC
2/sin45°=√6/sinC
2√2=√6/sinC
sinC=√3/2
∴∠C=120º或∠C=60º
∴∠A=15º或∠A=75º
∴sinA=(√6±√2)/4
S△ABC=½bc sinA=½x2x√6sinA=√6sinA=√6x(√6±√2)/4=(3±√3)/2
根据正弦定理得
b/sinB=c/sinC
2/sin45°=√6/sinC
2√2=√6/sinC
sinC=√3/2
∴∠C=120º或∠C=60º
∴∠A=15º或∠A=75º
∴sinA=(√6±√2)/4
S△ABC=½bc sinA=½x2x√6sinA=√6sinA=√6x(√6±√2)/4=(3±√3)/2