We discuss forward-backward charge asymmetries for lepton-pair production in association with a large-transverse-momentum jet at hadron colliders. The lepton charge asymmetry relative to the jet direction A(j)(FB) gives a new determination of the effective weak mixing angle sin((2)theta(lept)(eff)(M(2)(Z)) with a statistical precision after cuts of approximately 10(-3) (8x10(-3)) at LHC (Tevatron). This is to be compared with the current uncertainty at LEP and SLD from the asymmetries alone, 2x10(-4). The identification of b jets also allows for the measurement of the bottom-quark-Z asymmetry A(b)(FB) at hadron colliders, the resulting statistical precision for sin((2)theta(lept)(eff)(M(2)(Z)) being approximately 9x10(-4) (2x10(-2) at Tevatron), also lower than the reported precision at e(+)e(-) colliders, 3x10(-4).