Lesson 3 of 13
The Right Triangle
Almost every measurement problem in the trades turns out to be a right triangle wearing a different hat. Learn it once here and you will recognise it on a roof, in a footing, and inside a length of conduit.
Step one
Read the material
Three ideas. Each is something you will be asked to do.
Concept one
The legs and the hypotenuse
A right triangle has one square corner. The two sides that meet at that corner are the legs. The third side, the long one facing the square corner, is the hypotenuse.
That is the whole vocabulary. On a roof the legs are run and rise and the hypotenuse is the rafter. On a foundation the legs are the two walls and the hypotenuse is the diagonal. In a conduit offset the legs are the set and the run and the hypotenuse is the travel. Different trades, different words, same triangle.
Concept two
Finding the long side
Square each leg, add them, take the square root. That is the hypotenuse. Three and four give you five, because nine plus sixteen is twenty-five and the square root of twenty-five is five.
Any calculator will do it, including the one in your phone. What matters is knowing which two numbers to square. Square the wrong pair and the arithmetic is flawless and the answer is useless.
Concept three
Finding a missing leg
More often on a job you know the long side and one leg, and you need the other. Then you subtract instead of adding: square the hypotenuse, subtract the square of the known leg, take the square root of what is left.
A twenty foot ladder with its foot four feet out from the wall reaches up the square root of four hundred minus sixteen, which is 19 feet 7 1/2 inches. That is the same formula, run backwards, and it is the version that keeps people off the ground.
Step two
Work it with your hands on it
Set the two legs. The triangle redraws to scale and the hypotenuse is computed, never guessed.
Hands on it, off the screen. Take a tape into any room. Measure one wall, measure the wall it meets at the corner, then measure corner to corner across the floor. Set the sliders to your two walls and compare the hypotenuse to the diagonal you measured.
If they disagree by more than a little, the room is not square. That is lesson four.
Step three
Prove you understood it
One question per idea, new numbers every time. Miss one and the paragraph that covers it opens back up.
All three solid.
You can name the parts, find the long side, and find a missing leg. Lesson four puts that to work squaring a building.
Trades Geometry
Lesson three of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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