COSA=3/4,则COS C=2 COS²A-1=1/8.
所以sin A=√7/4,sin C=3√7/8.
COSB=-cos(A+C)= -cos A cos C+sin A sin C=9/16.
sinB=5√7/16.
向量BA*向量BC=27/2,则cacosB=27/2,
ca=24.
根据正弦定理得：a/sin A=c/ sin C,
所以a/sin A=c/ sin(2A),
a/sin A=c/[2sin A cos A],a=2c/3.
由此得a=4,c=6.
b/sinB=a/sinA,
b= a sinB /sinA=4 sinB /sinA=5.