Perpendicular by 3:4:5 Triangle

If you would rather avoid the square root calculations required in the Pythagorean Theorem method, you can apply the basic fact that any triangle with sides in the proportions of 3:4:5 is a right triangle. In locating point E, you know that this point lies 35 feet from C on a line perpendicular to the base line. You also know that a triangle with sides 30 and 40 feet long and a hypotenuse 50 feet long is a right triangle.

1. To get the 40 foot side, measure off 40 feet from C along the base line. In Figure 5-25, the segment from C to D happens to measure 40 feet.
2. Run a 50 foot tape from D and a 30 foot tape from C. The joined ends will lie on a line perpendicular from the base line, 30 feet from C.
3. Drive a hub at this point.
4. Extend the line to E, 5 more feet, by stretching a cord from C across the mark on the hub.