MHB Real world trigonometry problem making furniture

shane3
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I'm building a bed bench and I have an interesting trig problem that I can't figure out. I have a rectangle with known values and a parallelogram that bisects it with a known width. Like a board. I want to be able to figure out the angles so I can cut it. I want the board to intersect the rectangle in a specific way. I've attached an image as I have no other way to describe this. It feels like this should be solvable. Just not sure how. Any help would be great. Thanks.
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