The kinematic structure of remnants produced from major mergers of disk progenitors is examined. In particular, we consider moments of the projected velocity field and quantify departures of the line profiles from Gaussianity using a Gauss-Hermite expansion. By averaging over circular apertures, we are able to show that the line profiles exhibit significant deviations from Gaussianity and, of greater interest, we find that the high-order moments correlate with viewing angle. This effect appears to be a natural consequence of the orbital structure of equilibrium triaxial systems. The correlations in our models appear sufficiently tight that it may be possible, in principle, to infer viewing angles from observations, provided that the kinematics of the remnants in our simulations are representative of those of actual elliptical galaxies. Observational tests of our scheme are proposed, and possible applications of the technique to the study of intrinsic properties of galaxies and clusters are discussed.