正弦定理题目一道：A=60,a=12,则a+b+c/sinA+sinB+sinC=?

题目

正弦定理题目一道：A=60,a=12,则a+b+c/sinA+sinB+sinC=?

答案

a/sinA=b/sinB=c/sinC=2R
2R=a/sinA=12/sin60°=24/√3
(a+b+c)/(sinA+sinB+sinC)
=(2RsinA+2RsinB+2RsinC)/(sinA+sinB+sinC)
=2R
=24/√3
=8√3