sinB = 4cosAsinC
∴b/2R=4cosA? (c/2R)
Namely: b=4cosA? c
∴cosA=b/4c
According to cosine theorem: cosA=(b? +c? -a? )/2bc
∴(b? +c? -a? )/2bc=b/4c
4c? 【b? -(a? -c? )]=b? 200 BC
4c(b? -2b)=2b? c
4b? c - 8bc - 2b? c=0
2b? c - 8bc=0
2bc(b-4)=0
∵b≠0,c≠0
∴b-4=0, then b=4.