MHB Real world trigonometry problem making furniture

AI Thread Summary
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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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