图
(sinA)^2=(sinB)^2+(sinC)^2-sinBsinC
a^2=b^2+c^2-bc=b^2+c^2-2bc*cosA
cosA=1/2
A=60°
b/sinB=c/sinC=a/sinA=4
b+c=4(sinB+sinC)=6sin(B+C)/2 *cos(B-C)/2
=6*cos(A/2) *cos(B-C)/2
=3*(根号3) *cos(B-C)/2
所以：(3/2)*(根号3) < b+c <= 3*(根号3)
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