三角形ABC中,A=60度,a=2√3,则a+2b+3c与sinA+2sinB+3sinC的比值

问题描述:

三角形ABC中,A=60度,a=2√3,则a+2b+3c与sinA+2sinB+3sinC的比值

a/sinA=2√3/sin60=2√3/√2/2=4
则有
a/sinA=b/sinB=c/sinC=4
a/sinA=2b/2sinB=3c/3sinC=4
(a+2b+3c)/(sinA+2sinB+3sinC)=a/sinA=4