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Railroad Drawbridge Problem for Trigonometry Students

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A railroad drawbridge over a canal is to pivot upward, so boats can pass under it.

For trig students this is a good problem. The end-plate of the bridge span, where it lifts away from the rest of the track, cannot be due vertical in its rest position. If it were, the plate would jam as the span started to pivot. To allow clearance, the bottom edge of the plate must be canted slightly backwards toward the pivot point. Given the length a of the span and the height b of the plate, can you calculate the angle θ by which the plate must be canted from vertical?
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