We present distance determinations for two Local Group dwarf spheroidal galaxies, Carina and Fornax, based on the near-infrared magnitudes of the tip of the red giant branch (TRGB). For Carina we derive true distance moduli of 20.09 and 20.13 mag in the J and K bands, respectively, while for Fornax the same distance modulus of 20.84 mag was derived in both filters. The statistical errors of these determinations are of order 0.03-0.04 mag, whereas the systematic uncertainties on the distances are 0.12 mag in the J band and 0.14 mag in the K band. The distances obtained from the near-infrared TRGB method in this paper agree very well with those obtained for these two galaxies from optical calibrations of the TRGB method, their horizontal branches, RR Lyrae variables, and the near-infrared magnitudes of their red clumps.
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