在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
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![在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值](/uploads/image/z/1603929-57-9.jpg?t=%E5%9C%A8%E9%94%90%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2Cabc%E5%88%86%E5%88%AB%E4%B8%BA%E8%A7%92ABC%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%2C%E4%B8%94%E6%A0%B9%E5%8F%B73%E5%80%8DA%E7%AD%89%E4%BA%8E2%E5%80%8D%E7%9A%84c%E4%B9%98sinA%2C%E8%8B%A5c%E7%AD%89%E4%BA%8E%E6%A0%B9%E5%8F%B77%2C%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%BA2%E5%88%86%E4%B9%8B3%E5%80%8D%E6%A0%B9%E5%8F%B73%2C%E6%B1%82a%2Bb%E7%9A%84%E5%80%BC)
在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
解析:∵√3a=2csinA,c=√7
∴csinA=√3/2a
∵S(⊿ABC)=3√3/2=1/2bcsinA=1/2ab√3/2==>ab=6
由正弦定理a/sinA=c/sinC==>sinC=a/(csinA)=√3/2==>C=60°
由余弦定理c^2=a^2+b^2-2abcosC
∴a^2+b^2-ab=7=(a+b)^2-3ab=(a+b)^2-18
∴a+b=5
由√3a=2csinA,当c=√7时:
√3a=2√7sinA,
∴sinA=√3a/2√7=√21a/14.
△ABC面积S=(1/2)bcsinA
=(1/2)b×√7×√21a/14
=ba√3/4=3√3/2
∴ab=6.
a取2,b取3,△ABC是锐角三角形。
a+b=5.
(1)
由√3a=2csinA,当c=√7时:
√3a=2√7sinA,
∴sinA=√3a/2√7=√21a/14.
△ABC面积S=(1/2)bcsinA
=(1/2)b×√7×√21a/14
=ba√3/4=3√3/2
∴ab=6.
a取2,b取3,△ABC是锐角三角形。
a+b=5.
(2)
在锐角三...
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(1)
由√3a=2csinA,当c=√7时:
√3a=2√7sinA,
∴sinA=√3a/2√7=√21a/14.
△ABC面积S=(1/2)bcsinA
=(1/2)b×√7×√21a/14
=ba√3/4=3√3/2
∴ab=6.
a取2,b取3,△ABC是锐角三角形。
a+b=5.
(2)
在锐角三角形ABC中,abc分别为角ABC所对的边,且根号3倍A等于2倍的c乘
sinA,若c等于根号7,三角形ABC的面积为2分之3倍根号3,求a+b的值
解析:∵√3a=2csinA,c=√7
∴csinA=√3/2a
∵S(⊿ABC)=3√3/2=1/2bcsinA=1/2ab√3/2==>ab=6
由正弦定理a/sinA=c/sinC==>sinC=a/(csinA)=√3/2==>C=60°
由余弦定理c^2=a^2+b^2-2abcosC
∴a^2+b^2-ab=7=(a+b)^2-3ab=(a+b)^2-18
∴a+b=5
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