  Much of the information we hope to extract from the gravitational-waves
signatures of compact binaries is only obtainable when we can accurately
constrain the inclination of the source. In this paper, we discuss in detail a
degeneracy between the measurement of the binary distance and inclination which
limits our ability to accurately measure the inclination using gravitational
waves alone. This degeneracy is exacerbated by the expected distribution of
events in the universe, which leads us to prefer face-on systems at a greater
distance. We use a simplified model that only considers the binary distance and
orientation, and show that this gives comparable results to the full parameter
estimates obtained from the binary neutron star merger GW170817. For the
advanced LIGO-Virgo network, it is only signals which are close to edge-on,
with an inclination greater than $\sim 75^{\circ}$ that will be distinguishable
from face-on systems. For extended networks which have good sensitivity to both
gravitational wave polarizations, for face-on systems we will only be able to
constrain the inclination of a signal with SNR 20 to be $45^{\circ}$ or less,
and even for loud signals, with SNR of 100, the inclination of a face-on signal
will only be constrained to $30^{\circ}$. For black hole mergers observed at
cosmological distances, in the absence of higher modes or orbital precession,
the strong degeneracy between inclination and distance dominates the
uncertainty in measurement of redshift and hence the masses of the black holes.
