first of all.. us troops have never set foot in libya. we have provided air support alone.
secondly.. take these the two either-or scearios into consideration
two options= intervene or allow mass slaughter
two options= improve u.s. image in muslim countries by providing support for rebels after the league of arab nations requested it(the first time the league has ever approved of, let aloe requested u.s. intervention in a muslim country), or let the arab people believe the united states doesnt give a fuck about them unless we are going to get somehting out of it