A ballistic-electron spectroscopy, based on the scanning tunneling microscope, was used to probe the conservation of transverse crystal momentum at the Schottky barrier between polycrystalline metal and semiconductor. The Au/Si (111) interface is of particular interest because, for this orientation, all of the Si conduction-band minima will require a large transverse-crystal-momentum component for transmission. Here we demonstrate, using Monte Carlo calculations of ballistic-electron-emission microscopy (BEEM) currents which are compared with experimental data, that transverse momentum appears to be conserved for most of the observed BEEM current but that elastic scattering must be taken into acount. We show that this result implies that the spatial resolution of BEEM can vary greatly with substrate orientation and with the probability of elastic and inelastic scattering.