Splitting sloping walls?

[macfrog]

hi wrosun,

the "problem" was already solved before i started this thread. in first msg i wrote "i got a workaround" and i was asking for something easier i might have overseen.
i posted the picture just to let anybody see i donot ask for no reason; especially hans is very helpfull and spend some night with other peoples problems.
oh, and thanks for liking my model

[okh]

...intercept the meaning of the theorem...

Thanks Hans for your theorem interception, very useful. I think you mention something about doing the math in your much used roof guide. So as a hint, I took the liberty of putting a pointer to various calculations in SourceForge, feature-requests 684.

Maybe it is worth making a list of the most useful calculations for all of us who where not subjected to French maths in school? For instance, how to calculate the values indicated here, and probably a few more that I did not think of:
ok

[/

[Puybaret]

In your drawing, intercept theorem says that:

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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:

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2.48 = 1.6 + 2.2 x (3.4 - 1.6) / 4.5

If you replace 1.6 by heightAtStart, 3.4 by heightAtEnd, 4.5 by distanceBetweenStartAndEnd and 2.2 by distanceFromStart, you get:

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intermediateWallHeight = heightAtStart + distanceFromStart x (heightAtEnd - heightAtStart) / distanceBetweenStartAndEnd

Note 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:

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intermediateWallHeight = heightAtStart + distanceFromStart x tan(slopeAngle)

If you want to calculate that angle, just reverse the formula:

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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:

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4.85² = 1.8² + 4.5² = (3.4 - 1.6)² + 4.5²

If you replace 1.6 by heightAtStart, 3.4 by heightAtEnd and 4.5 by distanceBetweenStartAndEnd, you get:

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roofLength² = (heightAtEnd - heightAtStart)² + distanceBetweenStartAndEnd²

or:

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roofLength = sqrt((heightAtEnd - heightAtStart)² + distanceBetweenStartAndEnd²)

where sqrt is the square root.

Hope this will help [:)]

[okh]

Thanks a lot for this - and mostly for always paying attention to detail and answering every question. But I do feel guilty, it was not my intention to ask you to take the time to make the list. Checking my Pythagoras and basic trigonometry would certainly not do me any harm (even if I embarrassingly had to look up tangent being opposite/adjacent). That said, your explanation is, of course, better. And in any case, it always makes sense to check the maths of lawyers [:)] (As the joke goes: What can a goose do, a duck cannot, and a lawyer should? - Answer is where they can stick their bill...).

Anyway, this is the image I intended to post, trying to summarise hansmex' and the other posts on slopes and angles. Probably with unforgivable (and possibly erroneous) simplifications...

ok

[Puybaret]

Don't worry, I'm glad you found my answer useful [:)]
Just a small detail that bothers me on your drawing: visually, the ends of the green line don't seem to measure the top and the bottom of the same wall. You should add a small green line to join the top of intercepting wall. Hope you see what I mean...

[okh]

Yes, it bothered me too. I meant to move the entire green line, but forgot in the haste. Work in progress. To be improved. Thanks.

[okh]

Hmm, I did update the image, but forgot to link it here, still a rough sketch, though:

[mazaya]

That's an ingenious but simple workaround

[okh]

A different take on the same issue continued in thread 5953 with an interactive tool: Sloping wall intercept ok