  We have obtained single-phase near-infrared (NIR) magnitudes in the J- and
K-bands for 77 RR Lyrae (RRL) stars in the Fornax Dwarf Spheroidal Galaxy. We
have used different theoretical and empirical NIR period-luminosity-metallicity
calibrations for RRL stars to derive their absolute magnitudes, and found a
true, reddening-corrected distance modulus of 20.818 +/- 0.015 (statistical)
+/- 0.116 (systematic) mag. This value is in excellent agreement with the
results obtained within the Araucaria Project from the NIR photometry of red
clump stars (20.858 +/- 0.013 mag), the tip of the red giant branch (20.84 +/-
0.04 +/- 0.14 mag), as well as with other independent distance determinations
to this galaxy. The effect of metallicity and reddening is substantially
reduced in the NIR domain, making this method a robust tool for accurate
distance determination at the 5 percent level. This precision is expected to
reach the level of 3 percent once the zero points of distance calibrations are
refined thanks to the Gaia mission. NIR period-luminosity-metallicity relations
of RRL stars are particularly useful for distance determinations to galaxies
and globular clusters up to 300 kpc, that lack young standard candles, like
Cepheids.
