Chapter 1.2, Problem 46E

Carpentry Technique The following technique is used by carpenters to draw a 60° angle with a straightedge and a compass. Why does this technique work? (Source: Hamilton, J. E. and M. S. Hamilton, Math to Build On, Construction Trades Press.)

“Draw a straight line segment, and mark a point near the midpoint. Now place the tip on the marked point, and draw a semicircle. Without changing the setting of the compass, place the tip at the right intersection of the line and the semicircle, and then mark a small arc across the semicircle. Finally, draw a line segment from the marked point on the original segment to the point where the arc crosses the semicircle. This will form a 60° angle with the original segment.”