  The quantitative spectral analysis of medium resolution optical spectra of A
and B supergiants obtained with DEIMOS and ESI at the Keck Telescopes is used
to determine a distance modulus of 24.93 +/- 0.11 mag for the Triangulum Galaxy
M33. The analysis yields stellar effective temperatures, gravities,
interstellar reddening, and extinction, the combination of which provides a
distance estimate via the Flux-weighted Gravity--Luminosity Relationship
(FGLR). This result is based on an FGLR calibration that is continually being
polished. An average reddening of <E(B-V)> ~ 0.08 mag is found, with a large
variation ranging from 0.01 to 0.16 mag however, demonstrating the importance
of accurate individual reddening measurements for stellar distance indicators
in galaxies with evident signatures of interstellar absorption. The large
distance modulus found is in good agreement with recent work on eclipsing
binaries, planetary nebulae, long period variables, RR Lyrae stars, and also
with HST observations of Cepheids, if reasonable reddening assumptions are made
for the Cepheids. Since distances based on the tip of the red giant branch
(TRGB) method found in the literature give conflicting results, we have used
HST ACS V- and I-band images of outer regions of M 33 to determine a TRGB
distance of 24.84 +/- 0.10 mag, in basic agreement with the FGLR result. We
have also determined stellar metallicities and discussed the metallicity
gradient in the disk of M33. We find metallicity of $Z_\odot$ at the center and
0.3 $Z_\odot$ in the outskirts at a distance of one isophotal radius. The
average logarithmic metallicity gradient is -0.07 +/- 0.01 dex kpc^-1. However,
there is a large scatter around this average value, very similar to what has
been found for the HII regions in M33.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies