How to apply the 3-4-5 rule to create a right angle

One of the challenges when creating angles is ensuring they are square. While the room doesn't necessarily need to be perfectly square, the angles should be as close to 90 degrees as possible. Otherwise, when laying tiles or carpeting, you will immediately notice any discrepancies. The 3-4-5 method is also useful for small carpentry projects, helping all parts fit together as planned.

You need to understand the 3-4-5 method. If a triangle has sides of 3, 4, and 5 cm (or any other unit), it is definitely a right triangle with a 90º angle between the two shorter sides. If you "spot" this triangle at the measurement point, the angle between the two shorter sides is guaranteed to be right. This is based on the Pythagorean theorem from Geometry: in a right triangle, A² + B² = C². Where C is the longest side (the hypotenuse), and A and B are the two shorter sides (the legs).

• The 3-4-5 method is very convenient for verification because these are small positive integers. According to the Pythagorean theorem, we have: 3² + 4² = 9 + 16 = 25 = 5².

Begin by measuring three units of length (optional) from the corner to one side. You can use meters, centimeters, or any unit of measurement. Mark the point at the end of the 3-unit measurement.

• You can multiply each value by the same factor and still use the method. Try measuring 30-40-50 cm if using the metric system. For larger rooms, consider using the 6-8-10 or 9-12-15 meter sets.

Next, measure 4 units along the adjacent side. Use the same unit of measurement and measure the second side at a right angle to the first side. Mark the point where the 4-unit measurement ends.

Measure the distance between the two marked points. If this distance equals 5 units, the angle between the two sides is a right angle.

• If the distance is less than 5 units, the angle is smaller than 90º. Move the two sides further apart.
• If the distance is greater than 5 units, the angle is greater than 90º. Move the two sides closer together. You can use a framing square or square ruler to guide the adjustment.
• Once you achieve the right angle, check the other three corners of the room for similar results.