MHB Real world trigonometry problem making furniture

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The discussion revolves around a trigonometry problem related to building a bed bench, specifically involving a rectangle and a bisecting parallelogram. The user seeks to determine the angles needed for cutting a board that will intersect the rectangle in a specific manner. They express confidence that the problem is solvable but are unsure of the approach. An image is provided to clarify the geometric setup. Assistance is requested to solve this practical trigonometric challenge.
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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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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