  We present a reanalysis of the light curves of HD 23642, a detached eclipsing
binary star in the Pleiades open cluster, with emphasis on a detailed error
analysis. We compare the masses and radii of the two stars to predictions of
stellar evolutionary models and find that the metal and helium abundances of
the Pleiades are approximately solar. We present a new method for finding
distances to eclipsing binaries, of spectral types A to M, using the empirical
calibrations of effective temperature versus surface brightness given by
Kervella et al. (2004). We use the calibration for K-filter surface brightness
to determine a distance of 139.1 +/- 3.5 pc to HD 23642 and the Pleiades. This
distance is in excellent agreement with distances found from the use of
theoretical and empirical bolometric corrections. We show that the
determination of distance, both from the use of surface brightness relations
and from the use of bolometric corrections, is more accurate and precise at
infrared wavelengths than at optical wavelengths. The distance to HD 23642 is
consistent with that derived from photometric methods and Hubble Space
Telecscope parallaxes, but is inconsistent with the distance measured using
Hipparcos parallaxes of HD 23642 and of other Pleiades stars.
