I am trying to figure out the layout for a concrete slab, and it has introduced a mathematical question I cannot figure out.
Assume I want to pour a concrete slab that is 20 feet long by 40 feet wide, against a foundation. I want to put a single datum point on the foundation, against which I want to measure a uniform pitch, in this case 1 inch drop for each 4 feet in distance.
If I pull a line from the datum point, perfectly parallel to the 20 feet length of the slab, I will decrease in elevation by 5 inches if I follow the 1" per 4' pitch.
My question is this: Can I pull a line from the datum point, at the same 1" for 4' pitch, through any other point along the width of the slab, and still be measuring the same drop as the parallel measurement?
My intuition is that it should work, since the pitch as measured by the level will be the same irrespective of the distance.
However, when I calculate the elevation change for the midpoint of the width of the slab, it's 7" instead of 5", since now I am pulling the pitch across the 28' hypotenuse of the triangle, vs the 20' leg. Will this point, 7" below the datum at 28' distance, be level with the point 5" below the datum at 20' distance? Or do I need to always measure the pitch parallel with the slab to ensure the slab is level across its width?
