Calculating angles for wood joinery

Discussion in 'Geometry and Trigonometry' started by GregJ7, Nov 5, 2022.

  1. GregJ7

    GregJ7

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    This is an actual problem I have faced in woodworking and am now facing it again, and figure I ought to understand how to think about this problem geometrically, which is the problem I'm having. I have some wood boards that are initially similar to these in the first picture. It would be simple to join them by cutting each end at a 45° angle.
    Flat Boards.jpg

    However, they will not be laying flat (that is, Z=0 for all bottom edges). The bottom face will be tilted up A° from the outside such that the inside edges are raised above the Z=0 plane. (A = 30° in the picture.) My goal is to cut the ends of the boards with the same angles such that the cut edges will join face to face. After the boards are tilted up, B cannot have been cut at 45° if the faces are the join. Also, the cut edge is no longer 90° from the face (like the other 3 edges on each board). How do I calculate B and C given an angle A? Essentially, the cut faces need to be parallel to the Z-axis. The purpose of this calculation is because the boards can only be held steady when laying flat and it is the saw blade that must have its angle adjusted—but to what? Thanks for any help orienting my thinking for this problem! (and the final formula)
    Angled Boards.jpg
     

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    GregJ7, Nov 5, 2022
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