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See the image below:

When I lay this out in Fusion, I can get the angles but I can't figure out how to calculate it mathematically.

The goal is to have the angled stretcher fully contact the upper 45"-long support and the floor(even though there will be excess to remove.)

I'm looking for a formula for calculating the stretcher angle (35.8 in this case) and the length that the 2x4 would have to be.

I know how to calculate all of the angles of a right triangle, but no combination or the dimensions of the project give the correct angle.

Work Table

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  • duplicate of engineering.stackexchange.com/questions/38271/… – fred_dot_u Oct 21 '20 at 20:05
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    The tradition in woodworking, which, *cough*, was done for years before there was CAD (or even working drawings!) is to mark things like these angles directly from the workpiece. These days this is still sound practice in many woodworking contexts because tolerances are usually not very exact, and ~0.5mm variations aren't at all unusual. – Graphus Oct 22 '20 at 8:29
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    Yup, I agree with @Graphus. Put the calculator down, lay out the legs (attach them firmly, even), then drop the brace in place, line it up where you want it, clamp it down, and grab a pencil or scribe and mark it. Take it to the miter box & line up the blade with the marks by eye, and cut it a smidge proud. Test fit & adjust as necessary. When you're done, get the protractor and see what angle you cut. ;) – FreeMan Oct 22 '20 at 11:25
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    @Graphus if there was a situation where the layout was impossible due to location like if this were being done on a built-in, etc... – Mr. Mascaro Oct 22 '20 at 12:10
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    "if there was a situation where the layout was impossible due to location" ok sure, but this isn't one of those situations is it....? If you want to actually get this done, rather than have an Answer in the abstract, then do it the 'old fashioned' way. And see, the thing is if you do go ahead and calculate the angle and do all the cutting by the numbers, because that's how you think this should be done, the diagonal brace might not fit as well! It wouldn't be uncommon for two 'matching' diagonals to not be exactly the same on the built piece, which is why relative marking is so valuable. – Graphus Oct 23 '20 at 7:16
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Here's a solution I wrote over on the engineering site where this problem is cross-posted.

For anyone who may want to actually use this formula without evaluating the trig, here is a worksheet where you can enter the width of board you want to use, together with the length and height of the rectangle you need to span, and it finds a cut angle and the length of board you'll need.

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