1. Place a stake in the ground at the river's edge (B) and find a reference point on the other side (A).

2. Pace out a line along the shore at right angles to AB, and place a stake in the gound (C).

3. Now back away from the river's edge at right angles to BC. The longer this line is the more accurate your measurement will be. Place a stake at the end of the line (D).

4. Carefully mark the point (E) along the line BC that lies directly in line of sight between A and D. Now you have created two triangles: ABE and ECD.

5. Since the angles ABE and ECD are right angles, and angles AEB and CED are equal, then the two triangles have the same shape (they are "equiangular") and their sides are proportional. (Euclid VI, 4) By measuring the sides of one you can calculate the sides of the other. Let's say that the sides of ECD are 10 feet along the river and 5 feet back. For triangle ABE, you measure the side along the river (BE) to be 50 feet, five times as long as EC. So the leg of the triangle that crosses the river is five times the size as its counterpart on shore.

The distance across the river equals five times CD or 25 feet. And you didn't even get wet.