I would say it's the adjacent side, it would be unusual to describe the hypoteneuse when it would be much easier to describe the adjacent
ALL dimensions are given as horizontal & vertical - or vertical & horizontal - NEVER diagonal.
Stair Step: tread & riser
Roof Pitch: Horizontal Distance & Vertical Distance
Sewer Flow: 1% (translates to 1 foot vertical drop per 100 feet horizontal travel).
These are the easiest methods to layout & build.
Most carpenters use the slope/hypotenuse ONLY as a check -- never to setup to build.
In your question you are give the vertical rise over a horizontal distance.
The 20m is the adjacent side.
"A driveway is built on a slant where it rises 3m over a distance of 20m, what is the angle of elevation with the ground?I'm not sure if the 20m should be the adjacent leg or the hypotenuse."
in a civil engineer arena, you do measure base and height
grade = y/x = height/base
height = 3 m
base = 20
not necessary: slant height = sqrt (20^2 + 3^2) = sqrt 409 = 20.22375 m
angle of elevation = arctan (grade) = arctan (y/x) = arctan(height/base) = ?
you may read this: Grades, Highway | Macmillan Mathematics Summary