From a sample of 150 000 hadronic Z decays collected with the ALEPH detector at LEP, events containing prompt leptons are used to measure the forward-backward asymmetries for the channels and , giving the results AFBb=0.126±0.028±0.012 and AFBc=0.064±0.039±0.030. These asymmetries correspond to the value of effective electroweak mixing angle at the Z mass sin2θW(mZ2) = 0.2262±0.0053.