  We present a new method to derive binary inclinations in quiescent black hole
(BH) X-ray transients (XRTs), based on the depth of the trough (T) from
double-peaked Ha emission profiles arising in accretion discs. We find that the
inclination angle (i) is linearly correlated with T in phase-averaged spectra
with sufficient orbital coverage (>~50 per cent) and spectral resolution,
following i (deg)=93.5 x T +23.7. The correlation is caused by a combination of
line opacity and local broadening, where a leading (excess broadening)
component scales with the de-projected velocity of the outer disc.
Interestingly, such scaling allows to estimate the fundamental ratio M1/Porb by
simply resolving the intrinsic width of the double-peak profile. We apply the
T-i correlation to derive binary inclinations for GRO J0422+32 and Swift
J1357-0933, two BH XRTs where strong flickering activity has hindered
determining their values through ellipsoidal fits to photometric light curves.
Remarkably, the inclination derived for GRO J0422+32 (i=55.6+-4.1) implies a BH
mass of 2.7+0.7-0.5 Msun thus placing it within the gap that separates BHs from
neutron stars. This result proves that low-mass BHs exist in nature and
strongly suggests that the so-called "mass gap" is mainly produced by low
number statistics and possibly observational biases. On the other hand, we find
that Swift J1357-0933 contains a 10.9+1.7-1.6 Msun BH seen nearly edge on
(i=87.4+2.6-5.6 deg). Such extreme inclination, however, should be treated with
caution since it relies on extrapolating the T-i correlation beyond i>~75 deg,
where it has not yet been tested.
