  We present K-band interferometric and optical spectroscopic observations of
Menkar obtained with the instruments VINCI and UVES at Paranal Observatory.
Spherically symmetric PHOENIX stellar model atmospheres are constrained by
comparison to our interferometric and spectroscopic data, and high-precision
fundamental parameters of Menkar are obtained. Our high-precision VLTI/VINCI
observations in the first and second lobes of the visibility function directly
probe the model-predicted strength of the limb darkening effect in the K-band
and the stellar angular diameter. The high spectral resolution of UVES allows
us to confront observed and model-predicted profiles of atomic lines and
molecular bands. We show that our derived PHOENIX model atmosphere for Menkar
is consistent with both the measured strength of the limb-darkening in the
near-infrared K-band and the profiles of spectral bands around selected atomic
lines and TiO bandheads. At the detailed level of our high spectral resolution,
however, noticeable discrepancies between observed and synthetic spectra exist.
We obtain a Rosseland angular diameter of Theta_Ross=12.20 mas pm 0.04 mas.
Together with the Hipparcos parallax, it corresponds to R_Ross=89 pm 5 R_sun,
and together with the bolometric flux to T_eff=3795 K pm 70 K.Our approach
illustrates the power of combining interferometry and high-resolution
spectroscopy to constrain and calibrate stellar model atmospheres. The
simultaneous agreement of the model atmosphere with our interferometric and
spectroscopic data increases confidence in the reliability of the modelling of
this star, while discrepancies at the detailed level of the high resolution
spectra can be used to further improve the underlying model.
