Wave data from the DE 1 satellite showing simultaneously nonducted whistlers and hiss are analyzed to determine wave propagation directions. At L=3.8 and a geographic latitude of &lgr;g=12¿S, the average wave normal directions of discrete whistlers are measured to be ~51¿ for f=4.5 kHz and ~60¿ for f=3.5 kHz, forming a small (<20¿) angle with the magnetic meridional plane. Hiss wave normal angles are determined as ~70¿ and ~77¿ for f=3.5 kHz and f=2.5 kHz, respectively, with the wave vector being almost perpendicular to the meridional plane. While the measured wave normal angles of whistlers and hiss are consistent with generation of hiss by magnetospheric whistlers, existence of a significant azimuthal component indicates that further assessment of this connection must be based on three-dimensional ray tracing. A new approximate analytical formulation of three-dimensional propagation of whistler waves is developed and used to model the drift of magnetospherically reflected whistlers in azimuth. The results show that depending on initial parameters, the time of arrival of whistler rays at a fixed observation point can differ by 10--20 s, with signals from different magnetospherically reflected whistlers overlapping to evolve into a hiss like signal. The total azimuthal drift of whistler rays is found to not exceed ~30¿, so that plasmaspheric hiss may be produced by nonducted whistlers at longitudes correlated with the location of thunderstorm activity. ¿ American Geophysical Union 1993