Why do fighter planes fly at great heights?
Most fighters average around 50,000 feet as their ceilings and this isnt exactly a great height. Some of the answerers have correctly pointed out that the fighter can fly more efficiently at altitudes because of the smaller drag. Adding to that, heights also means potential energy. In combat you can trade altitude for airspeed and this has many benefits. For example when shot from 40K feet the missiles can have some extra range by virtue of their potential energy. Altitude also gives extended radar range (greater LoS) and will in turn reduce the effective ranges of the opponents missiles as those missiles would have to climb and climbs consumes lots of rocket fuel. Finally, flying high isnt always the chosen option, if possible the fighters would fly real low, attempting to evade enemy radar detection. High or low, it all depends on the mission needs.
