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
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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