cosA=3/4 sinA=√7/4
sinC=sin2A=2sinAcosA=3√7/8
cosC=cos2A=cos^2A-sin^2A=1/8
cosB=-cos(A+C)=-cosAcosC+sinAsinC=-3/32+21/32=9/16
向量BA*向量BC
=|BA|*|BC|*cosB=27/2
|BA|*|BC|=24
正弦定理
BA/sinC=BC/sinA
2BA=3BC
BA=6 BC=4
余弦定理
AC^2=BA^2+BC^2-2BA*BC*cosB=36+16-2*6*4*9/16=25
AC=5