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I want to cut a Scalene triangle: A triangle with no congruent sides out of plywood to fill in an open space in the roof sheathing. I can't trace it from underneath; there are trusses in the way.

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Step 1: cut the hole into a rectangle.

If you can't do that, pick a side to be your base. This side will correlate to a factory edge of the sheet. Ideally your sheet will be oriented correctly with respect to its strength axis.

Measure the length if the base side. Now measure precisely the lengths of each adjacent side, from each end of your base side.

Mark the base side dimension on the edge if your sheet from a corner. From that corner, strike an arc at a distance of the first adjacent dimension. From the base length mark, strike an arc that crosses the first arc at a distance of the second adjacent dimension. If you measured precisely, this will be your third corner. There's a lot of opportunity for error with this technique, which is why a rectangle is better.

Here's a diagram that shows the idea. Ignore the labels.

enter image description here

Another problem with triangles is long unsupported seams. You may want to float some backing and screw it all together to be sure that you don't put a foot through it later.

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    That is one of the two ways I verify the shape or dimensions of something like that. The other way is using a framing square and a straightedge to extend the leg of the framing square pointing to the upper end (apex?) of the triangle. Mark that location on the base and reproduce it on the material to cut to verify if the apex in remotely in the same spot, noting the dimensions of everything as I go... – Jack Feb 27 '18 at 0:26
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Iteration. Use cheap or waste material to make a test article. The most ideal material is paper but it may be unwieldy. Test fit that to the space. Note any errors. Correct those on another test article. Rinse wash repeat, you often get it in 2 and almost always in 3.

Copy those dimensions to the final material.

I'm fond of adding a step where I first model it in Adobe Illustrator, spam it with a layer of X's for positioning if I have to print multiple tiles, then either use the paper direct as the test article, or use it as a cutting guide.

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