在三角形ABC中,A=60度,a=3,求三角形ABC周长最大值,面积范围.

b/sinB=c/sin(120°-B)=a/sinA=3/(√3/2)=2√3三角形ABC周长=a+b+c=3+2√3sinB+2√3sin(120°-B)=3+2√3sinB+2√3*(√3/2cosB+1/2sinB)=3+3√3sinB+3cosB=3+6(√3/2sinB+1/2cosB)=3+6sin(B+π/6)当B=π/6时,即 A=B=C...