Compact binary mergers are the strongest candidates for the progenitors of short gamma ray bursts (SGRBs). If a gravitational wave signal from the compact binary merger is observed in association with a SGRB, such a synergy can help us understand many interesting aspects of these bursts. We examine the accuracies with which a worldwide network of gravitational wave interferometers would measure the inclination angle (the angle between the angular momentum axis of the binary and the observer's line of sight) of the binary. We compare the projected accuracies of gravitational wave detectors to measure the inclination angle of double neutron star and neutron star-black hole binaries for different astrophysical scenarios. We find that a five-detector network can measure the inclination angle to an accuracy of ∼5.1 (2.2) deg for a double neutron star (neutron star-black hole) system at 200 Mpc if the direction of the source as well as the redshift is known electromagnetically. We argue as to how an accurate estimation of the inclination angle of the binary can prove to be crucial in understanding off-axis GRBs, the dynamics and the energetics of their jets, and help the searches for (possible) orphan afterglows of the SGRBs. © 2014 American Physical Society.