How is the Pythagorean Theorem Used in Construction?

March 17, 2024

The Pythagorean theorem is more than just a fun mathematical exercise. It’s used in construction, manufacturing, navigation and many other fields to help create accurate measurements and right angles. For example, it’s used to calculate the distance of a lighthouse from a ship at sea.

The theorem states that the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the hypotenuse (the third side of the triangle). Builders use this fact on a daily basis when they build buildings. For example, when a roof has a certain pitch, it’s easy to find the required rafter size using the theorem. This helps to ensure that the roof is constructed properly.

Another application is ensuring that walls and foundations are straight. Builders often use the 3-4-5 special triangle to achieve this. To do so, they peg a string down where they want the corner of a wall to be and then measure a multiple of 3—say 6 feet—from the point to another spot that is also a multiple of 3, say 12 feet. The resulting triangle will have a square corner, which will give them confidence that their walls are being built straight.

The Pythagorean theorem underpins our system of measurement and allows for precise calculations that are critical in construction, manufacturing, navigation and many other field such as physics, geology, engineering and carpentry. It’s even believed to have been used in the construction of Stonehenge, which is thought to be over 2,000 years old!

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