The Use of Trigonometric Theorem in Elementary Mathematics in Everyday Life

Trigonometry makes use of the fact that proportions of sets of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right-angled triangle. The term trigonometry essentially implies the measurement of triangles. Trigonometry is a branch of mathematics that evolved from simple measurements.

A theorem is the most crucial concept in all of elementary mathematics. It was the inspiration for a wealth of advanced mathematics, such as Fermat’s Last Theorem and the theory of Hilbert space.

The Pythagorean Theorem asserts that for a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. There are several ways to prove the Pythagorean Theorem. An especially simple one is the scaling relationship for areas of similar shapes.

Did Pythagoras discover the Pythagorean Theorem or did he compile it by studying ancient cultures like Egypt, Mesopotamia, India and China? What did these ancient cultures know about the theorem? Where was the theorem used in their cultures? In ‘Geometry and Algebra in Ancient Civilizations’, the author discusses who first discovered the Pythagorean Theorem. He quotes Proclus, a commentator of Euclid’s Elements, stating that if we listen to those who wish to recount ancient history, we might find some who attribute this theorem to Pythagoras and say that he sacrificed an ox in honor of his discovery. If this statement is considered a declaration of fact, it is highly unlikely, since Pythagoras was opposed to the sacrificial slaughter of animals, especially cattle. If the saying is considered a legend, it is easy to explain how such a legend could have come into existence. Perhaps the first version of the legend stated that he who discovered this famed number sacrificed a bull in honor of his discovery.

Van der Waerden continues to comment that he believes the original discoverer was a priest from before the time of Babylonian texts who was allowed to sacrifice animals and was also a mathematician. This question can never be definitively answered, but evidence that cultures used the theorem prior to the time of Pythagoras can be found.

The theorem is useful in everyday life. For example, at a certain time of day, the sun’s rays cast a three-foot shadow from a four-foot flagpole. Knowing these two lengths, and the fact that the pole forms a ninety-degree angle with the ground, the distance from the end of the shadow to the top of the pole can be found without measuring. The first step is to substitute the given data into the actual formula. Now you can find the length of the third side, which is five feet. Trigonometry is essentially the study of the relationship between the sides and the angles of right-angled triangles. Knowing how to use these relationships and proportions is absolutely essential for just about everything. It might not seem like it, but trigonometry is used almost everywhere.

Another example of the importance of the theorem is the global sphere symbol, which represents engineering studies. Though there are many parts to this symbol, the Pythagorean theorem is effectively at the center, as much of engineering, measurement, logarithms and so on are based on trigonometric functions.

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