What atomic or hybrid orbitals make up the sigma bond between br and f in bromine trifluoride, brf3?

Draw the Lewis structure. Bromine has 3 bonds and two lone pairs for a trigonal bipyramidal electron geometry and an sp^3d hybridization. Fluorine is peripheral it does not require hybridization, but we often consider it to be hybridized too - it has 1 bond and 3 lone pairs for sp^3 hybridization. So the sigma bonds come from an overlap of an sp^3d orbital on Br with an sp^3 orbital on F. If you don't consider the F to be hybridized the overlap would have to be to a p orbital on the F