Question

已知A,B,C是是三角形ABC 的三个内角,A,B,C对的边分别为a,b.c,设平面向量m=(cos B,-sin C)

Answer 1

m*n=cos BcosC- sin Csin B=2/3

cos (B+C)=2/3

cosA=-2/3

sin A=√5/3

S△ABC =1/2bcsin A＝√5,sin A=√5/3

bc＝6

a^2=b^2+c^2-2bccosA

9=b^2+c^2+2*6*2/3

b^2+c^2=1

(b+c)^2=1+2bc=1+12=13

b+c=√13