WWII Experts! Over Here! I've Got A Question!!!!!?

OK. During WWII, the US Army has 3 types of cap badges. A small one on a round disc, a large one for officers w/o a disc. and another one for officers thats more triangular shaped. It seems that USAAF officers wore them, but I've seen regular Army officers wear them too. Who is it exactly that wore the the triangular shaped officers badge?