Thanks, everyone.
Warrior's estimate of 30-40 degrees and repcisg's diagram showing 45 degrees are pretty close to my estimate of 45 degrees. Since my calculator is at work and since I hate the non-RPN calculator on the computer, I'll try to a finish the calculation that drove this question in the next day or so, and will share my findings if they make any sense. Of course, it's been a long time since I took dynamics, and since I hated that class anyway (despite receiving an A in it), I may have blocked it out to the point of remembering absolutely nothing. I guess that is why most engineers keep all their textbooks!
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"Tilting at the SciFi windmill"
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