Real world trigonometry problem making furniture

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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.
View attachment 9223
 
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  • Diagram of a rectangle 12 inches wide and 24 inches tall with two diagonal boards crossing in an X, one labeled 1 1/2" wide and an angle to find marked at the top left.
    trigproblem.png
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see diagram ...
 
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  • Diagram of a rectangular frame with a red diagonal brace from corner A to corner C, labelled 12 inches across the top and 24 inches down the right side, with a 1 1/2 inch wide strip and points A, B, C, D, E marked, and the angle theta at A.
    angle_measure.jpg
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