三角形ABC的三个内角A,B,C对应的三条边长分别是a,b,c,且满足csinA+根号3acorC=

三角形ABC的三个内角A,B,C对应的三条边长分别是a,b,c,且满足csinA+根号3acorC=

(1) sinA/a=sinC/ccsinA=asinCcsinA+√3acosC=0asinC+√3acosC=02a(1/2sinC+√3/2cosC)=02asin(C+π/3)=0∵a≠0∴sin(C+π/3)=0C+π/3=πC=2π/3(2) ∵C=2π/3∴A+B=π/3sinA=√(1-cos²A)=√(1-(3/5)²)=4/5sin(A+B)=sinπ/3sinAcosB+cosAsinB=√3/24/5√(1-sin²B)+3/5sinB=√3/28√(1-sin²B)+6sinB=5√38√(1-sin²B)=5√3-6sinB64-64sin²B=75-60√3sinB+36sin²B100sin²B-60√3sinB=11100(sinB-3√3/10)²=11+27sinB-3√3/10=±√37/10sinB=(3√3±√37)/10∵B∴sinB=(3√3+√37)/10b/sinB=c/sinCb=5√3/sin(2π/3)*(3√3+√37)/10=(√3(3√3+√37)/2)/(√3/2)=3√3+√37======以下答案可供参考======供参考答案1:csinA+根√3acosC=0 2(1/2*sinCsinA+√3/2*sinAcosC)=0 2sinA(1/2*sinC+√3/2*cosC)=0 2sinA*sin(C+60)=0 sinA=0 A=90sin(C+60)=0 C+60=90 C=30(2)cosA=3/5，c=5√3sinA=4/5c/sinC=a/sinA=b/sinB5√3/(1/2)=a/(4/5)a=8√3b=√(a方+c方-2accosC)=19√5sinB=(19√15)/30

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