Question

有关正弦定理结论的证明如图这是百科里的介绍,求证明为什么a/sinA=(a+b)/(sinA+sinB)=(a+b+c)

Answer 1

设a/sinA=b/sinB=c/sinC=k

则有a=sinA*k,b=sinB*k,c=sinC*k

∴(a+b)/(sinA+sinB)=(sinA*k+sinB*k)/(sinA+sinB)=k=a/sinA=b/sinB=c/sinC

∴(a+b+c)/(sinA+sinB+sinC)=(sinA*k+sinB*k+sinC*k)/(sinA+sinB+sinC)=k=a/sinA=b/sinB=c/sinC