  Gamma-ray burst (GRB) prompt emission is highly beamed, and understanding the
jet geometry and beaming configuration can provide information on the poorly
understood central engine and circum-burst environment. Prior to the advent of
gravitational-wave astronomy, astronomers relied on observations of jet breaks
in the multi-wavelength afterglow to determine the GRB opening angle, since the
observer's viewing angle relative to the system cannot be determined from the
electromagnetic data alone. Gravitational-wave observations, however, provide
an independent measurement of the viewing angle. We describe a Bayesian method
for determining the geometry of short GRBs using coincident electromagnetic and
gravitational-wave observations. We demonstrate how an ensemble of
multi-messenger detections can be used to measure the distributions of the jet
energy, opening angle, Lorentz factor, and angular profile of short GRBs; we
find that for a population of 100 such observations, we can constrain the mean
of the opening angle distribution to within 10 degrees regardless of the
angular emission profile. Conversely, the constraint on the energy distribution
depends on the shape of the profile, which can be distinguished.
