由正弦得:asinB=bsinA
∵√3b=2asinB
∴√3b/2=asinB=bsinA
∴sinA=√3/2
∵三角形是锐角三角形
∴A=60
∴cosA=1/2
∵a/sinA=b/sinB=c/sinC
∴b=asinB/sinA=4√3sinB
c=asinC/sinA=4√3sinC
∵sinB=sin(A+C)=sin(60+C)
∴sinB=√3/2cosC+1/2sinC
∴b+c=4√3(sinB+sinC)
=4√3(√3/2cosC+1/2sinC+sinC)
=6cosC+6√3sinC
=12sin(C+π/6)
∵A=60
∴C∈(0,2π/3)
∴C+π/6∈(π/6,5π/6)
∴sin(C+π/6)∈(1/2,1]
∴b+c∈(6,12]
有不明白的地方欢迎追问.
在锐角三角形ABC中角A,B,C所对的边分别为a,b,c,已知根号3b=2asinB,求角的大小;若a=6,求b+c的范围
在锐角三角形ABC中角A,B,C所对的边分别为a,b,c,已知根号3b=2asinB,求角的大小;若a=6,求b+c的范围
数学人气:913 ℃时间:2019-08-21 11:50:38
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