Let's say we hike a mile straight up or down a 30 degree slope. I know this is almost dangerously steep, but the numbers work easy.

If I accurately pace my distance. But on the map, I've only moved .87 miles. Which will the GPS show? My impression is it will show the mile.

If I marked the start as a waypoint and I hiked in a straight line, will the distance to the waypoint show as .87 miles or 1 mile?

This only matters over long distances. The Appalacian Trail is 2,187 miles long. Is that according to the map? Or is that according to miles walked. If the average slope is 7 degrees, there is a 10% difference.

Maybe I woke up too early this morning.