Just wanted to provide you with some information supplemental to the ID provided by Lloyd Gonzoles. Insect body length is customarily measured from the front of the head (excluding antennae) to the end of the abdomen (excluding tails). Based on your estimate of 38 mm. (including length of tails), I believe your mayfly would have a body length of 16.5 mm.

Incidentally, only the middle tail of a mayfly imago is called a terminal filament. The outer tails are referred to as cerci. In the case of Hexagenia in its winged form, the terminal filament is vestigal (an appendage surviving in a dwarfed or degenerate form), and can be barely seen in the cast shadow when zooming in on your 3rd photo.

Although limbata would seem likely, a few of the variants of that highly variable species are very difficult to distinguish from rigida. These could be separated by the shape of the genitalia of a male imago. Both species are found in parts of OK.