We describe a method of determining the system parameters in non-eclipsing interacting binaries. We find that the extent to which an observer sees the shape of the Roche lobe of the secondary star governs the amount of distortion of the absorption-line profiles. The width and degree of asymmetry of the phase-resolved absorption-line profiles show a characteristic shape, which depends primarily on the binary inclination and gravity darkening exponent. We show that, in principle, by obtaining high spectral and time resolution spectra of quiescent cataclysmic variables or low-mass X-ray binaries in which the mass-losing star is visible, fitting the shape of absorption-line profiles will allow one to determine not only the mass function of the binary, but also the binary inclination and hence the mass of the binary components.