(sinA)^2+(cosA)^2=1与sinA+4cosA=4联立解方程
17(cosA)^2-32cosA+15=0
cosA=1(A=0,舍去) cosA=15/17
sinA=8/17
sinA/a=sinB/b=sinC/c=(sinB+sinC)/(b+c)
(8/17)/a=(4/3)/(b+c)
b+c=(17/6)a
△ABC中O是外接圆的圆心,OA=OB=OC=3 ∠BOC=2∠BAC
cos∠BOC=(OB^2+OC^2-BC^2)/2OB×OC=(3^2+3^2+a^2)/2×3×3=(18-a^2)/18
cos∠BOC=cos2A=(cosA)^2-(sinA)^2=(15/17)^2-(8/17)^2=161/289
(18-a^2)/18=161/289
a=48/17
b+c=(17/6)a=(17/6)×(48/17)=8
bc
S=(1/2)bcsinA=(1/2)bc×(8/17)