Eccentric Ellipsoidal Red Giant Binaries in the LMC Ellipsoidal red giant binaries contain a red giant or AGB star and a small, close companion which distorts the shape of the primary, causing photometric variations in these non-contact binaries. The descendents of these variables may be planetary nebulae with binary central stars. Roughly 10% of these ellipsoidal red giants have light curves with non-sinusoidal shapes, suggestive of eccentric orbits. We studied a sample of these red giant ellipsoidals in the Large Magellanic Cloud, and presented the first radial velocity curves confirming their eccentricity. By orbital modelling we were able to determine the exact masses of both components, despite the absence of eclipses. We also find evidence that the shape of the red giant changes throughout the orbit due to the high eccentricity and the varying influence of the companion. Defining the parameters of these systems paves the way for modelling to determine by what mechanism eccentricity is maintained in evolved binaries.