Question

在三角形ABC中，sin∠ABC/2=根号3/3，AB=2，点D在线段AC上，且AD=2DC， BD=4根号3/3，则BC等于多少？

Answer 1

设CD=m ∠ADB=a
sin(∠ABC/2)=根号3/3 cos(∠ABC/2)=根号6/3
sin∠ABC=2sin(∠ABC/2)cos(∠ABC/2)=2根号2/3
cos∠ABC=1/3
由余弦定理 cosa=(4x^2+16/3-4)/(16√3m/3)
cos(180°-a)=-cosa=(x^2+16/3-BC^2)/(8√3m/3)
两式相加4x^2+16/3-4+2x^2+32/3-2BC^2=0
3x^2=BC^2-6 (1)

Answer 2

20