  Heartbeat stars are eccentric (e > 0.2) ellipsoidal variables whose light
curves resemble a cardiogram. We present the observations and corresponding
model of KIC 3749404, a highly eccentric (e = 0.66), short period (P = 20.3 d)
heartbeat star with tidally induced pulsations. A binary star model was created
using PHOEBE, which we modified to include tidally induced pulsations and
Doppler boosting. The morphology of the photometric periastron variation
(heartbeat) depends strongly on the eccentricity, inclination and argument of
periastron. We show that the inclusion of tidally induced pulsations in the
model significantly changes the parameter values, specifically the inclination
and those parameters dependent on it. Furthermore, we determine the rate of
apsidal advance by modelling the periastron variation at the beginning and end
of the 4-yr Kepler data set and dividing by the elapsed time. We compare the
model with the theoretical expectations for classical and general relativistic
apsidal motion and find the observed rate to be two orders of magnitude greater
than the theoretical rate. We find that the observed rate cannot be explained
by tidally induced pulsations alone and consequently hypothesise the presence
of a third body in the system.
