Question

1.已知A、B、C是△ABC的三个内角,其对边分别为a、b、c,若向量m=(-cosA/2,sinA/2),向量n=(c

Answer 1

1、m·n=-cos^2A/2+sin^2A/2=-cosA=1/2

cosA=-1/2 则sinA=根号3/2

S=1/2bcsinA=根号3 有bc=4

余弦定理：b^2+c^2-2bccosA=a^2

代入 有b^2+c^2=8

(b+c)^2=b^2+c^2+2bc=16

故b+c=4

2、正弦定理：b=asinB/sinA c=asinC/sinA

b+c=a(sinB+sinC)/sinA=4(sinB+sinC)

A=2/3π

B+C=π/3 b+c=4(sinB+sin(1/3π-B))

=4(根3/2cosB+1/2sinB)=4sin(B+π/3)

又0