If we can safely assume a 1 meter ramp is 45 degrees, we work down in halves from there. So the half ramp is 22.5 degrees and takes 2 meters to reach a full 1 meter of height. Cut in half again and its 11.25 degrees and takes 4 meters to reach 1 meter in height. Vertex positions on the incline on the 3 blocks are at 1.0, .5, .25.
That's not how right angled triangles work.
Tan = Opposite/Adjacent
This means that for a slope of angle X, tan(X) = height of block/length of blocks
If the angle is 45°, then tan(X) = tan(45°) = 1 (you can check that on your calculator!)
Therefore with a 45° angle, the slope is 1 block high and 1 block long. That's obvious, but we're just confirming the maths.
However, for a 22.5° angle, tan(X) = tan(22.5°) = 0.4142
Therefore with a 22.5° angle, the slope is
not half a block high for every block long; it is 0.4142 blocks high for every block long.
So a slope that is two blocks long to one block high cannot be at a 22.5° angle.
To find out what angle a slope two blocks long and one block high is, we have to solve:
tan(X) = 1/2
Therefore X = tan-1(0.5)
Plugging that into a calculator gives us: X = 26.565°
So a slope that is two blocks long to one block high is actually at an angle of 26.565°, not 22.5°.
(And by the same method, a four long one high slope is at an angle of tan-1(0.25) = 14.036°, not 11.25°)
@Roland - can you mark my homework for me, please?