  The measurement of obliquities in star-planet systems is of great importance
for the understanding of planet system formation and evolution. The bright and
well studied HAT-P-7 system is intriguing as several Rossiter-McLaughlin (RM)
measurements found a large projected obliquity in this system, but it was so
far not possible to determine if the orbit is polar and/or retrograde. The goal
of this study is to measure the stellar inclination and hereby the full 3D
obliquity of the HAT-P-7 system instead of only the 2D projection as measured
by the RM effect. In addition we provide an updated set of stellar parameters
for the star. We use the full set of available observations from Kepler
spanning Q0-Q17 to produce the power spectrum of HAT-P-7. We extract
oscillation mode frequencies via an MCMC peak-bagging routine, and use the
results from this to estimate the stellar inclination angle. Combining this
with the projected obliquity from RM and the inclination of the orbital plane
allows us to determine the stellar obliquity. We use asteroseismology to model
the star from the extracted frequencies using two different approaches to the
modelling where either the MESA or the GARSTEC stellar evolution codes are
adopted. Using our updated asteroseismic modelling we find, i.a., the following
stellar parameters for HAT-P-7: M=1.51{+0.04}{-0.05}Msun,
$R=2.00{+0.01}{-0.02}Rsun, and age = 2.07{+0.28}{-0.23} Gyr. Our asteroseismic
modelling offers a high precision on the stellar parameters, for instance is
the uncertainty on age of the order ~11%. For the stellar inclination we
estimate i_star<36.5 deg., which translates to an obliquity between 83 and 111
deg. We find that the planet HAT-P-7b is likely retrograde in its orbit, and
that the orbit is close to being polar. The new parameters for the star gives
an updated planetary density of 0.65+-0.03 g cm^{-3}, which is lower than
previous estimates.
