Having never done any carpentry nor googled the answer, the first thing that's coming to mind is to place the board at the angle you want, then use a straight edge (like a level) extended out from the floor of the upper story to trace a line on the board. Cut the board, then flip it over so that cut side is on the bottom, and then repeat the process to cut the top.
Edit: I guess my first line will read as a disclaimer if I'm wrong (aka missing an important detail!) or a brag if I'm right; it's intended as the former!
I think you've got a slight problem with this approach, that a diagram should illustrate if you draw the board as a rectangle and not a line. Thought experiment time:
Let us assume that you rest the board in such a manner that the angle between the edge of the board and the vertical wall is 45 degrees. The edge of the board is tangential to the corner of the wall and the upper floor, and you scribe the horizontal line, then cut it.
When you now flip the board around so that the cut you made will rest flush against the ground, the other end will still be a line that's tangential to the 90-degree join between wall and upper floor; it won't be flush against the wall.
For a 45 degree angle, you could go "oh, I'll just scribe a vertical line upwards where the board is tangential to the corner, and cut it." When you do this, you'll find the board may be flush to the ground, but it extends past the first floor, because you basically cut it too long. You could, by careful repeated cutting, shave off enough from the bottom to get it to fit flush to the floor, and flush to the wall... but that's a lot of cutting.
Now, you could apply some simple (?) maths here, and realise that for a 45 degree angle, the answer is that the board has to be some multiple of square_root(2) long, but that's maths, and that's not allowed. :)
Back to the physical approach. What if we did that horizontal cut, then rotated the board so that it became a vertical cut? Well, now it should be flush against the wall, but the end on the ground is resting on the corner of the board, not a face. You could cut it so that the "back" (furthest from the wall) corner was flush to the ground, but now the top of the board will be a few inches lower than the upper story.
This is non-trivial :) It gets worse if you're not using a 45 degree angle which makes things symmetrical.
Another problem with reality: most wall-floor angles are not exactly 90 degrees! Anyone who has tried to build custom cabinetry and shelving can attest to this.
Ah yes. I thought through it picturing the diagram in my head rather than looking at it. In my mental picture the board was sitting on top of the edge of the top floor, rather than coming up to flush with it. Which obviously doesn't make sense in retrospect!
What's coming to mind next is a horizontal cut as first described (placing at the angle you want). Flip, then vertical cut, and finally trim the end with the horizontal cut by making a parallel cut offset by the amount the board extends above the upper floor. I'm sure there's a better way though. Non-trivial indeed. :)
Further thinking.. instead of scribing a horizontal line, scribe a vertical one at the top, cut that. Then scribe a horizontal line from the back corner towards the wall, cut that. Should then fit flush to both ground and wall.
I should go find a bit of paper and scissors and try.
Edit: I guess my first line will read as a disclaimer if I'm wrong (aka missing an important detail!) or a brag if I'm right; it's intended as the former!