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A River Runs Through It

Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it; and at each end of this line, I found angles subtended by the other end and a tree close to the bank on the other side of the river to be \(53^\circ\) and \(79^\circ 12'\).  What is the perpendicular breadth of this river?

A Course of Mathematics, Charles Hutton, 1816

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"A River Runs Through It," Convergence (July 2006)