In a scattering environment, the propagation paths to a receiving antenna arrive from a certain angular spread of directions. For a low-resolution antenna, an apparent direction of arrival may be defined as the azimuth direction of maximum power. A small array is used as the antenna and the spatial derivative of the phase along the array axis is taken as a measure of the sine of the apparent angle of arrival. The sine of the angle is shown to be Student's t-distributed and from this result the PDF and power spectrum of the angle-of-arrival is determined. The distributions are compared with experimental results for indoor as well as for outdoor measurements.