Luca wanted to make a bench.

a sketch of a bench with an arc drawn on the backrest of the bench
Figure8.3.23Sketch of a Bench with Highlighted Back

He wanted the top of the bench back to be a perfect portion of a circle, in the shape of an arc, as in FigureĀ 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?

the bench backrest board labeled 48 in by 3 in and a large circle that makes the arc on the board;there is a dot in the center of the circle
Figure8.3.24Bench Back Board