Originally Posted by
BluesDawg
I could easily be getting in over my head here

, but the reason I used the hypotenuse was to take known values (the distance traveled and the elevation gain) to solve the unknown value (the run).
Rise over run works and is so simple, it is what we use to determine departure climb gradients in air transport. Whether the GPS thinks the world is flat doesn't matter a damn. Can I lose an engine and still get me and the passengers and crew over that hill is all that counts!

If it is good enough for that, it is good enough for riding a bike.