Often, when builders want to lay the foundation for the corners of a building, one of the methods they use is based on the Pythagorean Theorem (serious!).  In the previous pages we explored some special right triangles.  One of them is the 3-4-5 triangle.

Builders use this special triangle (or a multiple of it, say, 9-12-15) when they don't have a carpenter's square (an instrument for constructing right angles) handy.

This is the process they follow:

• First, they peg a string down where they want a specific wall to be.
• Then, they measure (in feet usually) a length of the string that is a multiple of three, say two times three, and mark that off (so they would be marking off a section that was six feet long).  Call the marked endpoints points A and B, where B is where the corner is to be built.
• Where they want the corner to be (point B) they attach another piece of string.  If we are basing this method on the Pythagorean Theorem and using the special 3-4-5 right triangle, what do you think the length of the second side should be?  Why? (click here for the answer).
• Then, using the Pythagorean Theorem as their guide, they attach a piece of string at point A that corresponds to what the length of the hypotenuse of a right triangle of side lengths 6 and 8 feet respectively would be.  What do you think that length should be?  (click here for the answer).  Why?
• Lastly, they bring the ends of the second and third pieces of strings together.  Why do you think they do that?
• Voila!  We now have a right angle where we want the corner to be courtesy of the Pythagorean Theorem!