⑴ ∠C=90º+∠A.2∠A=90º-∠B,cos2∠A=sin∠B=1/3
sin∠A=√[(1-1/3)/2]=1/√3.
⑵ BC/sin∠A=AC/sinB,BC=3√2.sinC=sin(A+B)=√(2/3)
S⊿ABC=(1/2)×AC×BCsinC=3√2(面积单位)
⑴ ∠C=90º+∠A.2∠A=90º-∠B,cos2∠A=sin∠B=1/3
sin∠A=√[(1-1/3)/2]=1/√3.
⑵ BC/sin∠A=AC/sinB,BC=3√2.sinC=sin(A+B)=√(2/3)
S⊿ABC=(1/2)×AC×BCsinC=3√2(面积单位)