Pythagoras and SketchUp, Model a Wacky Room

Most good builders know and use the Pythagorean Theorem, even if they never heard of Pythagoras or slept through high school geometry. It’s easier to remember 3-4-5 than an ancient Greek and it’s a reliable way to make something at an exact 90-degree angle to something else. Measure three feet out from one corner and four feet from the other corner, then measure diagonally from point to point. When the two points are five feet apart, the corner is square. When you encounter a structure put together by a guy who didn’t know this, or one that has suffered from the ravages of time, you can use the trick in reverse to accurately duplicate the angle.

Let’s say we’re trying to fit cabinets in an existing room, and field measurements of 36″ on one wall and 48″ on the other reveal a distance of 61-1/4″ across the points. Before you go out and buy a digital angle finder, try this in SketchUp:

Step 1 Pythagorean Theorem in SketchUpDraw a line on-axis, 36″ long. From one end of the line, draw a circle with a 48″ radius. After you click to start the circle, look for an axis inference as you drag the cursor to create the circle. That will leave the cardinal points of the circle in the right place. If you measure from the other end of the line to the edge of the circle, at the cardinal point, the Tape Measure tool will display 60″, proof that Pythagoras knew what he was talking about.

Pythagorean Theorem in SketchUp Step 2From the other end of the line make another circle using the field measurement of 61-1/4″. The intersection of the two circles will fall on the angled line we’re trying to reproduce.Pythagorean Theorem in SketchUp Step 3Connect the end of the first line and the intersection of the two circles with a line. This line will be slightly shorter than 48″, due to the fact that SketchUp creates circles as 24-sided polygons. If that concerns you, you can change the number of segments SketchUp uses to make the circle. For most uses, any error in the angle will be insignificant.

Pythagorean Theorem in SketchUp Step 4Get the Eraser tool and remove the arcs. That will leave you with the original line, parallel with a horizontal axis, and the angled line. If you like, you can use the Protractor tool to place a guideline along the angled line to complete the model. You can also use the Protractor to make guidelines at 90-degrees to the angled line to help you see how square cabinets will fit in the angled corner.

345_5SketchUp will also display on inference that matches the angled line as seen in the image above. After you click to start a new line, let go of the mouse button and trace over the angled line for a few seconds. SketchUp will figure out what you’re trying to do, and show a magenta inference when you move past the end of the angled line.

Bob Lang

If SketchUp is “all Greek to you”, check out my books or SketchUp classes.


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