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# How do architects use the Pythagorean theorem?

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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.

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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.

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## Related Questions

• A:

A major advantage of arch bridges is the fact that they are structurally sound for short spans, while a major disadvantage includes the amount of building materials needed to construct an arch bridge, even if it is of short length. Other advantages of arch bridges include the inexpensive costs of building materials such as stone and brick, and the ability to build more arches to span a wider distance.

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For medium distances of between 500 and 2,500 feet, cable-stayed bridges have the advantages over suspension bridges of requiring less steel cable and being less expensive and quicker to build. In addition, instead of being limited to two towers as suspension bridges are, cable-stayed bridges can be built with any number of towers.

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Arch bridges resist compression extremely well, while suspension bridges provide the best tensile strength. Since compression and tension are opposite in nature, it is not possible to guarantee that one type of bridge is the strongest against both.