△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3除以3,求BC的长;求三角形DBC的面积?△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3/3,求BC的长;求三角形DBC的面积?
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![△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3除以3,求BC的长;求三角形DBC的面积?△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3/3,求BC的长;求三角形DBC的面积?](/uploads/image/z/1693316-20-6.jpg?t=%E2%96%B3ABC%E4%B8%AD%2Csin%28%E2%88%A0ABC%2F2%29%3D%E2%88%9A3%2F3%2CAB%3D2%2C%E7%82%B9D%E5%9C%A8%E7%BA%BF%E6%AE%B5AC%E4%B8%8A%2C%E4%B8%94AD%3D2DC%2CBD%3D4%E2%88%9A3%E9%99%A4%E4%BB%A53%2C%E6%B1%82BC%E7%9A%84%E9%95%BF%3B%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2DBC%E7%9A%84%E9%9D%A2%E7%A7%AF%3F%E2%96%B3ABC%E4%B8%AD%2Csin%28%E2%88%A0ABC%2F2%29%3D%E2%88%9A3%2F3%2CAB%3D2%2C%E7%82%B9D%E5%9C%A8%E7%BA%BF%E6%AE%B5AC%E4%B8%8A%2C%E4%B8%94AD%3D2DC%2CBD%3D4%E2%88%9A3%2F3%2C%E6%B1%82BC%E7%9A%84%E9%95%BF%3B%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2DBC%E7%9A%84%E9%9D%A2%E7%A7%AF%EF%BC%9F)
△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3除以3,求BC的长;求三角形DBC的面积?△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3/3,求BC的长;求三角形DBC的面积?
△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3除以3,求BC的长;求三角形DBC的面积?
△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3/3,求BC的长;求三角形DBC的面积?
△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3除以3,求BC的长;求三角形DBC的面积?△ABC中,sin(∠ABC/2)=√3/3,AB=2,点D在线段AC上,且AD=2DC,BD=4√3/3,求BC的长;求三角形DBC的面积?
由余弦定理 cosa=(4m^2+16/3-4)/(16√3m/3)
cos(180°-a)=-cosa=(m^2+16/3-BC^2)/(8√3m/3)
两式相加4m^2+16/3-4+2m^2+32/3-2BC^2=0
3m^2=BC^2-6 (1)
又由余弦定理AC^2=AB^2+BC^2-2AB*BCcos∠ABC
9m^2=4+BC^2-4BC*1/3
27m^2=12+3BC^2-4BC (2)
联立(1)(2) BC=3 (对的,你对)
三角形ABC的面积=(1/2)AB*BCsin∠ABC
=(1/2)*2*3*2√2/3
=2√2
三角形DBC的面积=(1/3)三角形ABC的面积=2√2/3