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 hypothesize the presence of a third body in the system.
