The Pytagorean Theorum says that in a right triangle, the sum of the squares of the length of the 2 sides (adjacent to the right angle) is equal to the squre of the hypotenuse.
A simplified version of this for construction workers is based on the fact that this formulation comes out with nice even numbers when any multiple of the ratio 3:4:5 is used (9+16=25).
Thus if a building is say 44 feet long by 40 feet wide, the lay-out would begin on the straight 44' side. a measurement of 33' from one end of it "eyeball close" to perpendicular would be pulled and an arc swung maybe 3-5 feet long at that measurement.
Then from the opposite corner of the 44' wall, a 55' measurement would be pulled to intersect with the arc just drawn. A string pulled from the origin of the 33' measurement through this intersection and on out to the 40" point would square these 2 walls to each other well within 1/4" tolerance.
Lay-out people will just as readily say "Let's pull a 3:4:5" as they will "let's square it up"
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Geometry is used mainly in construction.
a straightedge
There are both advantages and disadvantages to using the builder's square method. One advantage is that it is a relatively simple method to use and can be easily learned by most people. Another advantage is that it is a versatile method that can be used for a variety of projects, including construction, remodeling, and repairs. However, there are also some disadvantages to using the builder's square method. One of these is that it is not always accurate, and this can lead to errors in your project. Additionally, it can be time-consuming to use this method, especially if you are working on a large project.
a straightedge
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