Question

已知三角形ABC的三个内角ABC所对的三边分别是abc平面向量m=(1,sin(B-A)),平面向量n=(sinC-si

Answer 1

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据正弦定理,a/sinA=b/sinB=c/sinC=4/(sqrt(3)

即：a=4sinA/sqrt(3),b=4sinB/sqrt(3)

故周长L=a+b+c=2+(4/(sqrt(3))*(sinA+sinB)=2+(4/(sqrt(3)))*2sin((A+B)/2)cos((A-B)/2)

2+(8/(sqrt(3)))*sin(C/2)cos((A-B)/2)=2+4cos((A-B)/2)

因为,A+B=2π/3,所以,L=2+4cos(π/3-B)

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