过D作DF⊥BC于F点
sin角CBD=DF/BD=0.75,所以：DF＝BDsin角CBD=8*0.75=6
而AE⊥BC,知DF//AE,△CDF∽△CAE
所以：DF/AE＝CD/AC,可知：AE＝AC*DF/CD＝6*3/2＝9