Question

在△ABC中,角A,B,C所对的边分别为a,b,c,求满足cosA/2=(2根号5)/5,向量AB*向量AC=3.求△A

Answer 1

1.cosA/2=2√5/5 sinA/2=√5/5

sinA=2sinA/2*cosA/2=4/5 cosA=(cosA/2)^2-(sinA/2)^2=3/5

AB向量点乘AC向量=|AB|*|AC|*cosA=3

|AB|*|AC|=5

S=1/2*|AB|*|AC|*sinA=2

2.b+c=6

|AB|*|AC|=5 bc=5

余弦定理a^2=b^2+c^2-2bc*cosA

=(b+c)^2-2bc-2bc*cosA

=36-10-10×(3/5)

=20,

a=2√5.