Luca wanted to make a bench.
He wanted the top of the bench back to be a perfect portion of a circle, in the shape of an arc, as in Figure 8.3.24. (Note that this won't be a half-circle, just a small portion of a circular edge.) He started with a rectangular board \(3\) inches wide and \(48\) inches long, and a piece of string, like a compass, to draw a circular arc on the board. How long should the string be so that it can be swung round to draw the arc?