Question

已知三角形ABC中，角A=60度，a=根号3，a+b+c/sinA+sinB+sinC

Answer 1

根据正弦定理，a/sinA=b/sinB=c/sinC,
利用等比定理得：(a+b+c)/(sinA+sinB+sinC)= a/sinA
=根号3/sin60度=2.

Answer 2

∵在△ABC中
∴由正弦定理得a/sinA=b/sinB=c/sinC
故(a+b+c)/(sinA+sinB+sinC)=3×（a/sinA）=3×√3/(√3/2)=6