Architects use the Pythagorean theorem, which is expressed by the equation: a2 + b2 = c2, in designing and computing the measurements of building structures and bridges. One example involves roof design. A gable roof is made of two right triangles, where the base of one right triangle is called the run, the height is called the rise and the slope is called the rafter.

It's easy to compute the measurement of the required rafter of the roof using the Pythagorean theorem. To illustrate, if the roof calls for the pitch to have a 6-inch rise and 12-inch run, the rafter is equal to 13.4 inches when computed using the Pythagorean theorem.

In laying the foundation of a building, it is possible to make each corner a right angle, even without a carpenter's square, using only strings, the Pythagorean theorem, particularly the 3-4-5 special triangle and the architect's supervision. First, mark point A as the spot where a wall is to be built. Use a string to measure out a multiple of three, say 6 feet, and mark the endpoint as B, where B is the corner foundation. Use another string to measure a multiple of 4, say 8 feet, from point B to point C. This is the measure of the second wall. Then, a third string connects point C to A and the length should be 10 feet, a multiple of 5, to ensure that the corner is at a right angle.