Optical spectra were obtained of the optical counterpart of the high latitude soft X-ray transient XTE J1118+480 near its quiescent state with the new 6.5 m MMT and the 4.2 m WHT. The spectrum exhibits broad, double-peaked, emission lines of hydrogen from an accretion disk superposed with absorption lines of a K7V-M0V secondary star. Cross-correlation of the 27 individual spectra with late-type stellar template spectra reveals a sinusoidal variation in radial velocity with amplitude K = 701 +/- 10 km/s and orbital period P = 0.169930 +/- 0.000004 d. The mass function, 6.1 +/- 0.3 solar masses, is a firm lower limit on the mass of the compact object and strongly implies that it is a black hole. Photometric observations (R-band) with the IAC 0.8 m telescope reveal ellipsoidal light variations of full amplitude 0.2 mag. Modeling gives a large mass ratio (M1/M2 ~ 20) and a high orbital inclination (i = 81 +/- 2 deg). Our combined fits yield a mass of the black hole in the range M1 = 6.0-7.7 solar masses (90% confidence) for plausible secondary star masses of M2 = 0.09-0.5 solar masses. The photometric period measured during the outburst is 0.5% longer than our orbital period and probably reflects superhump modulations as observed in some other soft X-ray transients. The estimated distance is d = 1.9 +/- 0.4 kpc corresponding to a height of 1.7 +/- 0.4 kpc above the Galactic plane. The spectroscopic, photometric, and dynamical results indicate that XTE J1118+480 is the first firmly identified black hole X-ray system in the Galactic halo.
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