已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA 1 、求角A的大小 2、如果用psinA,sinBsinC已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA1 、求角A的大小 2、如果用psinA,sinBsinC为长度
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![已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA 1 、求角A的大小 2、如果用psinA,sinBsinC已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA1 、求角A的大小 2、如果用psinA,sinBsinC为长度](/uploads/image/z/5502651-51-1.jpg?t=%E5%B7%B2%E7%9F%A5%E2%96%B3ABC%E7%9A%84%E4%B8%89%E5%86%85%E8%A7%92A%2CB%2CC%E4%B8%8E%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9a%2Cb%2Cc%E6%BB%A1%E8%B6%B32b-c%2Fa%3DcosC%2FcosA+1+%E3%80%81%E6%B1%82%E8%A7%92A%E7%9A%84%E5%A4%A7%E5%B0%8F+2%E3%80%81%E5%A6%82%E6%9E%9C%E7%94%A8psinA%2CsinBsinC%E5%B7%B2%E7%9F%A5%E2%96%B3ABC%E7%9A%84%E4%B8%89%E5%86%85%E8%A7%92A%2CB%2CC%E4%B8%8E%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9a%2Cb%2Cc%E6%BB%A1%E8%B6%B32b-c%2Fa%3DcosC%2FcosA1+%E3%80%81%E6%B1%82%E8%A7%92A%E7%9A%84%E5%A4%A7%E5%B0%8F+2%E3%80%81%E5%A6%82%E6%9E%9C%E7%94%A8psinA%2CsinBsinC%E4%B8%BA%E9%95%BF%E5%BA%A6)
已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA 1 、求角A的大小 2、如果用psinA,sinBsinC已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA1 、求角A的大小 2、如果用psinA,sinBsinC为长度
已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA 1 、求角A的大小 2、如果用psinA,sinBsinC
已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA
1 、求角A的大小 2、如果用psinA,sinBsinC为长度的线段能围成以斜边的直角三角形,试求实数p的取值范围
已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA 1 、求角A的大小 2、如果用psinA,sinBsinC已知△ABC的三内角A,B,C与所对的边a,b,c满足2b-c/a=cosC/cosA1 、求角A的大小 2、如果用psinA,sinBsinC为长度
1、(2b-c)cosA-acosC=0
由正弦定理b/sinB=a/sinA=c/sinC=2R
b=2RsinB
a=2RsinA
c=2RsinC
(2b-c)cosA-acosC=0
2R(2sinB-sinC)cosA-2RsinAcosC=0
(2sinB-sinC)cosA-sinAcosC=0
2sinBcosA-sinCcosA-sinAcosC=0
2sinBcosA-(sinCcosA+sinAcosC)=0
2sinBcosA-sin(A+C)=0,
2sinBcosA-sin(180-B)=0,
所以:2sinBcosA-sinB=0,
因为:A、B∈(0,π),sinB≠0
所以:cosA=1/2,
所以:A=60度
2、sin^2 B+sin^2 C=p^2 sin^2 A
p^2=(sin^2 B+sin^2 C)/0.75
=(sin^2(120-C)+sin^2 C)/0.75
=(5-cos2C-根号3的sin2C)/3 (C在0到120之间)
=【5-2sin(2C+30°)】/3
∴P^2∈【1,7/3)
∴P∈【1,根号21 /3)