  The stellar inclination angle-the angle between the rotation axis of a star
and our line of sight-provides valuable information in many different areas,
from the characterisation of the geometry of exoplanetary and eclipsing binary
systems, to the formation and evolution of those systems. We propose a method
based on asteroseismology and a Bayesian hierarchical scheme for extracting the
inclination angle of a single star. This hierarchical method therefore provides
a means to both accurately and robustly extract inclination angles from red
giant stars. We successfully apply this technique to an artificial dataset with
an underlying isotropic inclination angle distribution to verify the method. We
also apply this technique to 123 red giant stars observed with
$\textit{Kepler}$. We also show the need for a selection function to account
for possible population-level biases, that are not present in individual
star-by-star cases, in order to extend the hierarchical method towards
inferring underlying population inclination angle distributions.
