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Geometry Problem
Okay, we all know the Pythagorean Theorem, right? A^2 +B^2 = C^2, fine. If we know the length of the hypotenuse and all three angles, how do we find the length of the other sides? My instruments are insufficiently precise to simply draw and measure the thing.

Data: Hypotenuse is 42.25 inches. Angles are 90, 89, and 1, and I need the length of the (very) short side.