PYTHAGOREAN THEOREM IN CONSTRUCTION
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
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
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!