Yes, I used trignometry to figure out the angles of the stairways and ramps in my dungeons. The only time I can think of I used those formulas after I graduated from high school.
To show the players the angles, I used an adjustable drafting triangle. I didn’t show the the side with the degree markings. That way they had to estimate the angle. If a dwarf was in the group, I let that character use their dwarf skills, depth underground, etc. to determine a range of the slope. So a 28 degree slope, the dwarf player rolled percentile dice. And if make the roll, against what ever ability I figured matched, I told them ‘the angle is between 25 and 30 degrees’… if they made the roll. If they failed, I gave a wider range, say 20 to 35 degrees.
Room 1: 10’ × 10’ × 15’
Nothing but dust in room 1. A few tree roots. Stone steps lead downward.
The stairs are 26’ long. At a 28.7 degree slope, and drop for 12 feet 6 inches.
Various tree roots, from the trees up on top, restrict movement in the passageway.
The corridor that now turns right is 20 feet long. It has a slight 2 degree slope that drops down a further 6 inches.
More stairs. Forty feet long, 30 degree slope for a drop of 35 feet.
Another right turn as the passageway drops further into the ridge.
This 40 foot long passageway drops 2 feet 1.2 inches on a 3 degree slope.
