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How Does the Pythagorean Theorem Work In The Real World?

To use real world examples with the Pythagorean Theorem.
by Brandon Lester on 26 April 2011

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Transcript of How Does the Pythagorean Theorem Work In The Real World?

How Does The PythagoreanTheorem Work In The Real World? Objective 1: To use the Pythagorean Theorem Objective 2: To identify right triangles Who invented the Pythagorean Theorem? The Pythagorean Theorem was invented by a Greek philosopher named Pythagoras. Pythagoras was born about 569 B.C. Pythagoras was also was known as the first true Mathematician. The Pythagorean theorem was a mathematical fact that the Babylonians knew and used. However 1000 years later, between the years of 580-500 B.C, Pythagoras was the first to prove the theorem. How the Pythagorean Theorem was first used. The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs


6 8 cm cm c c= a + b 2 2 2 c= 6 + 8 2 2 2 c=100 2 c= 100 = 10 The length of the hyptenuse is 10 cm. Today many people ask how we can use the Pythagorean Theorem in the real world. So here are some examples. Examples: Baseball Diamond, Height iof a building, Two friends meeting at a specific destination, Ramp of a moving truck, Measurement of a TV Firemen, construction workers, and other workers often rely on the use of ladders in their line of work. They make use of the Pythagorean Theorem in various situations. For example, the height to a second story window may be 25 feet, and a window cleaner may need to put the ladder ten feet away from the house in order to avoid the bushes or flowers. How long of a ladder does the window cleaner need in order to achieve this task? (25)^2 + (10)^2 = c^2, or the length of ladder needed. 625 + 100 = 725. The square root of 725 is approximately 27, so the window cleaner would need a ladder 27 feet long.


Let’s say Bob and Larry are meeting at Blockbuster on the corner of Park and Pleasant Street. Presently, Bob is on Park Street to and is 8 miles away. Meanwhile, Larry is on Pleasant Street 7 miles away. How far away are they from each other? (8)^2 + (7)^2 = distance between Bob and Larry. 64 + 49 = 113. The square root of 113 is approximately 10.6. Thus, this is how far apart Bob and Larry are from each other
Television sets are generally measured diagonally, thus classifying them as 13 inches, 27 inches, 36 inches, and so forth. Suppose we want to purchase an entertainment center, but it only holds enough room in it’s cubicle for a 27 inch TV set. We initially know that the length of our TV is 15 inches, and the height of our TV is 12 inches. Will our TV be able to fit into the cubicle? (15)^2 + (12)^2 = 369. The square root of 369 is approximately 19.2 inches. Therefore, our TV will fit with plenty of room to spare.


The height of a moving truck is 4 feet. The distance from the bottom edge of a ramp on the ground to the truck is 6 feet. How long is the ramp? (4)^2 + (6)^2 = length of ramp.

16 + 36 = 52. The square root of 52 is approximately 7.2, which is the length of the ramp.


The Pythagorean Theorem is used for many things in the world. Now that technology is advancing everyday machines and computers are used to calculate many things that relate to the Pythagorean Theorem such as, location. Google Earth can calcuate the exact location of any places useing the sateillet.
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