The Pythagorean Theorem can be used to solve numerous real world problems involving right-angled triangles where the lengths of at least two sides are known. One of the areas the theorem can be applied is in construction by painters. Since painters use ladders to reach high walls, the Pythagorean theorem would assist them in determining how tall their ladder should be in order for its base to be safely placed away from the wall such that it is stable and does not tip over. The walls are perpendicular to the ground, and the ladder is a hypotenuse, and this makes the Pythagorean theorem most appropriate for this application. The same technique is used by window cleaners, construction workers, and even firefighters. The measurements can be taken using a tape measure. The solution does not require additional geometric concepts, and there no simpler methods that could otherwise be applied apart from the Pythagorean theorem (brighthubeducation.com).
In engineering, the theorem can be used to calculate the internal and external forces acting on structural members, since forces are summed or subtracted using vectors. In this case, the Pythagorean theorem is only used when vector forces act on each other at right angles. The theorem would not be applicable in cases where the forces are not 90 degrees to each other, and other geometrical concepts such as trigonometrical ratios can be applied. The measurements for this kind of solution can be taken using a tape measure during the actual construction of structures such as girders, or a ruler can be used when drawing design diagrams and calculating the forces. In such a case, for vector addition at 90 degrees, the Pythagorean theorem is the most appropriate due to its simplicity (Physicsclassroom.com). There are modern methods of calculating forces during design especially when computer-aided engineering (CAE) design tools are used to design structures, but these also use Pythagorean theorem for computation.
Finally, the third use of Pythagorean theorem is in building construction to determine right angled corners. It works by first marking the point where the corner should be and placing a second mark on a predetermined line. Then a third final mark is placed in such a way that the distance from the other two forms a Pythagorean triplet, then it is confirmed that the corner is indeed a right angle. A tape measure is used to take the measurements and due to the simplicity of Pythagorean theorem, no other tools or geometrical concepts are necessary.
Works Cited:
Brighthubeducation.com. "Uses of Pythagoras's Theorem in Real Life Scenarios for Middle School Students". Bright Hub Education. N.p., 2016. Web. 20 June 2016. <http://www.brighthubeducation.com/homework-math-help/36639-applications-of-pythagoras-theorem-in-real-life/>.
Physicsclassroom.com. "Vectors - Motion and Forces in Two Dimensions - Lesson 1 - Vectors: Fundamentals and Operations: Vector Addition". Physicsclassroom.com. N.p., 2016. Web. 19 June 2016. <http://www.physicsclassroom.com/class/vectors/Lesson-1/Vector-Addition>.
