A whole lot of abstraction- given two longitude/latitude points given from a GPS, I'm using the Pythagorean distance formula to find the distance between them. What unit of length would the distance be? Kilometers? Miles?
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Just like any other function, you will get out the same unit of measurement you put in. In this example you are using lat/long and so will therefore get the distance between your two points (the hypotenuse) in degrees. The number of kilometers/miles/inches/whatever that the output corresponds to depends entirely on where on the surface of the earth the hypotenuse lies.
Also, it does not really matter in this instance that you are "pretending" the earth is flat. Along that note, if the earth was flat we wouldn't use lat/long as, again, those are ellipsoidal (angular) measurements. This is why we have map projections with grid based (cartesian) coordinate systems.