We present a model for determining the mass ratio in interacting binaries by directly fitting the observed spectrum with synthetic spectra. We make direct use of NEXTGEN model atmosphere intensities, which are the most comprehensive and detailed models available for cool stars. We fully take into account the varying temperature and gravity across the secondary star's photosphere, by incorporating the synthetic spectra into the secondary star's Roche geometry. As a result, we determine the exact rotationally broadened spectrum of the secondary star and so eliminate the need for a limb-darkening law, and the uncertainties associated with it. As an example we determine the mass ratio for the well-studied soft X-ray transient Nova Sco 1994. In order to obtain a more accurate determination of the mass ratio, which does not depend on assumptions about the rotation profile and limb-darkening coefficients, we use our model to compute the exact rotationally broadened model spectrum, which we compare directly with the observed intermediate resolution spectrum of Nova Sco 1994. We determine the mass ratio of Nova Sco 1994 to be 0.419 +/- 0.028 (90 per cent confidence), which is the most accurate determination of the binary mass ratio in an X-ray binary. This result, combined with the binary mass function and inclination angle, gives a refined black hole mass of 5.99 +/- 0.42 Msolar (90 per cent confidence). We also perform simulations which show that, for an F-type secondary star, the standard rotation profile with zero and continuum value for the line limb-darkening coefficient gives a value for q that brackets the value found using the full geometrical treatment.