Contractor wearing a tool belt measures right angle
If you never thought you’d use high school geometry again, that’ll change once you need to lay out right angles. (DepositPhotos)

Laying out accurate right angles on building projects — such as foundations for sheds, decks or patios — is easy if you use geometry.

According to the Pythagorean Theorem, the square of the two sides of a triangle that adjoin the right angle (legs) are equal to the square of the third side (hypotenuse). This is expressed mathematically as a² + b² = c².

To use, multiply the length of each leg of the triangle by itself then add the two sums together to find the length of the hypotenuse when the angle is at 90°.

The easiest way to accomplish this is to use the 3-4-5 method:

  • Measure 3 feet out from the angle you want to make 90° in one direction.
  • Measure 4 feet out from the angle you want to make 90° in the other direction.
  • Measure across the two points and adjust the angle until the distance on the third side of the triangle is 5 feet.

You can also use multiples of 3-4-5 in the same ratio (such as 6, 8, 10) to form larger or smaller right angles.

Watch this video to find out more.

Further Information

VIDEO TRANSCRIPT
Joe Truini: You might not have thought you’d ever get around to using high school geometry, but if you’ve ever had to lay out lines at a perfectly square, 90-degree corner, here’s a chance to use it.

If it’s a large project like this, where we’re extending the patio, a framing square would be too small; it wouldn’t be accurate enough. So we’re going to use the Pythagorean theorem and that’s based on a three, four, five ratio.

So along one line, I measured and marked three feet, and along the intersecting line I did the same thing, only at four feet. And now, to put the theorem into practice, you simply measure across the two lines and you move the stake, in or out, until the five-foot mark lines up exactly with the mark that you made on the line. Then you can drive in the stake.

And it won’t be perfectly in line the first time, but you can move the stake in or out, side to side, as you need to.

And this works — here I did it at three feet, four feet, five feet. But you can use any of those ratios, so it could be six, eight or 10. The larger the project, the larger the numbers, the more accurate it’ll be.

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6 COMMENTS

  1. I think you explained the getting the building square was correctly but you left out cross measuring to final check for square. Good job though i use the 6.8.10 myself it does work. (Nothing to do with this article but when laying first sheet of decking on roof at a 8 ft.break whole sheet nail one end in middle of rafter then adjust to chalk line then pull lay off sets rafter at a 90 very straight when done thanks guys just alittle what i know works after building 30 years

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