And the shooting was captured on a news helicopter camera, so there is a birds eye view of the whole incident, which should help to quickly clear the officers.
Hopefully no cop ever wants to shot someone, but if you have to, this is the perfect scenario. Suspect has hostage, suspect has already injured someone, suspect slips and hostage is able to create distance, hostage is stupid enough to continue to pursue hostage in front of multiple cops and, best of all, the whole incident is captured on high quality video feed.
Fellas, enjoy your time off and clear your heads of the incident. It is obvious that your decision was not only justified, but also neccessary. Who knows what this lunatic would have done if he wasn't shot and taken into custody.