Today’s Wonder of the Day was inspired by Carissa. *Carissa Wonders*, “**Why is the pythagorean theorem so important?**” Thanks for WONDERing with us, Carissa!

There are certain things you learn in school that you use on an everyday basis. Some of these things include reading, writing, spelling, and basic mathematics, such as addition, subtraction, multiplication, and division.

Then there are other things that you learn in school that you probably don't use every single day. How often do you need to know when World War I started? Does knowing the details of the process of photosynthesis come in handy every day?

How about all those esoteric mathematical concepts and formulas? Will algebra ever be useful in real life? Actually, you might be surprised how often you end up using algebra and other mathematical concepts without even realizing it.

Let's take a look at one of those formulas you may have learned about in school: the Pythagorean Theorem. The name makes it sound like something akin to advanced particle physics, but it's actually a fairly simple, straightforward way to calculate the length of the third side of a right triangle if you know the lengths of the other two sides.

The equation that derives from the Pythagorean Theorem is familiar to many: a^{2} + b^{2} = c^{2}. In this equation, c represents the longest side (known as the hypotenuse) of a right triangle. Reminder: a right triangle is a triangle that has one 90˚ angle.

The letters a and b represent the other two sides. Stated another way, the Pythagorean Theorem holds that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, if side a measures 3 and side b measures 4, you can calculate that side c will measure 5 (3^{2} + 4^{2} = 5^{2} or 9 + 16 = 25). It will help you to know how to calculate square roots, and you can also use basic algebra to figure out any missing side of a right triangle as long as you know two of its measurements.

The Pythagorean Theorem is credited to Pythagoras, who was a Greek philosopher and mathematician that lived in the 5^{th} century B.C. However, historians have discovered that other ancient civilizations knew about the basic mathematics of the Pythagorean Theorem thousands of years earlier.

For example, new studies show that the ancient pillars of Stonehenge may have been placed very precisely using the geometry of the Pythagorean Theorem. Although no one knows who built Stonehenge, historians believe it was constructed over 2,000 years before Pythagoras was born.

Does the Pythagorean Theorem have any usefulness in real life? You bet it does! First, it's often used as the basis for more complicated mathematics, including calculating areas, volumes, and perimeters of all sorts of geometric shapes.

On a day to day basis, you might find yourself using the Pythagorean Theorem in certain types of jobs and tasks. These might include architecture, construction, navigation, and surveying. Basically, any time you build something and you need to use square angles or know how long one side of a triangle needs to be, you'll be using the Pythagorean Theorem!

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Standards:
*CCRA.L.3, CCRA.L.6, CCRA.R.1, CCRA.R.2, CCRA.R.4, CCRA.R.10, CCRA.SL.1

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