In your drawing, intercept theorem says that:
4.5 / (3.4 - 1.6) = 2.2 / (2.48 - 1.6)as you probably look for the 2.48 height here, the previous formula isn't very handy, but you can change it like this:
2.48 = 1.6 + 2.2 x (3.4 - 1.6) / 4.5If you replace 1.6 by heightAtStart, 3.4 by heightAtEnd, 4.5 by distanceBetweenStartAndEnd and 2.2 by distanceFromStart, you get:
intermediateWallHeight = heightAtStart + distanceFromStart x (heightAtEnd - heightAtStart) / distanceBetweenStartAndEndNote that (heightAtEnd - heightAtStart) / bothWallsLength is a factor that could reapply elsewhere on walls with the same slope. This factor is also equal to tangent of 21.8°. Thus, if you know the 21.8° angle of the slope, you can also use:
intermediateWallHeight = heightAtStart + distanceFromStart x tan(slopeAngle)If you want to calculate that angle, just reverse the formula:
slopeAngle = arctan((heightAtEnd - heightAtStart) / distanceBetweenStartAndEnd)You might also wonder how to compute the 4.85 roof length. This time, it's Pythagorean theorem that will give you the answer because angles between walls and the floor are right:
4.85² = 1.8² + 4.5² = (3.4 - 1.6)² + 4.5²If you replace 1.6 by heightAtStart, 3.4 by heightAtEnd and 4.5 by distanceBetweenStartAndEnd, you get:
roofLength² = (heightAtEnd - heightAtStart)² + distanceBetweenStartAndEnd²or:
roofLength = sqrt((heightAtEnd - heightAtStart)² + distanceBetweenStartAndEnd²)where sqrt is the square root.
Hope this will help
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Emmanuel Puybaret, Sweet Home 3D creator
