The Pythagorean Theorem can be used in any real life scenario that involves a right triangle having two sides with known lengths. In a scenario where a certain section of a wall needs to be painted, the Pythagorean Theorem can be used to calculate the length of the ladder needed if the height of the wall and the distance of the base of the ladder from the wall are known.

The Pythagorean Theorem can be usefully applied because the relationship between the lengths of the sides in any right triangle is consistent. For example, in a baseball field, if the distance between each base is known, then the shortest distance to throw the ball from first base to third base can be calculated using the Pythagorean Theorem. When purchasing a television, the size advertised refers to the length of the diagonal of the television. As a member, you'll also get unlimited access to over 75, lessons in math, English, science, history, and more.

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- Explaining the Pythagorean Theorem with Models & Diagrams.

Joe the Fireman has to carry Maruto, the pound sumo wrestler, down a long ladder to the fire truck. If it's 40 feet to the ground and 60 feet from the building to the truck, how long is the ladder? Triangle problems that include a right angle are possibly the most common geometric math challenge that we're likely to see in real life. The Pythagorean theorem tells us that in a right triangle, the square of the length of the hypotenuse the side opposite the right angle is equal to the sum of the squares of the other two sides.

But how do you get that across to your students? How do you get them to become so comfortable with the principles involved that they can automatically use them, like a familiar hammer or pair of scissors? Two good ways to do that involve diagrams , or pictures that illustrate the concept, and models , or real-life challenges that involve the concept under study. Diagrams allow you to point out relationships within a concept. For example, using the Pythagorean Proof diagram, you can illustrate a visual proof for the theorem, giving the students a real reason to believe that the theorem actually works.

Once they have a feel for how it works, they then will much more easily make it a part of their repertoire. You can show the students a diagram of a graphed right triangle.

### Laying Out Square Angles

You can then expand it out to something like the Triangle Squares diagram, which is on your screen now and which shows what squares you're talking about. As you explain that the area inside the two smaller squares adds up to the larger square, you may find that some students don't think that's true. That's when you can pull out the Pythagorean Proof squares to illustrate, and have the students cut out triangles and fit them in to see it work. Models can be a lot of fun for the students, and can create memorable experiences that cement the conceptual and procedural learning into their minds.

When you're trying to teach them to use the Pythagorean theorem, you can give them a real-life problem to solve, one that will require the use of the theorem. Remember, the more real the model is, the more valuable it will be in reinforcing the learning. One fantastic application involves building a bridge across a ravine. This model can be great for applying the Pythagorean theorem to vectored force discussions, as well as structural lengths and distances.

The idea is to have the students use craft sticks or some other simple materials to build a weight-bearing bridge between two surfaces, such as desks or tables. The students may not run any pillars to the bottom of the ravine, so they'll need to form triangles to support the bridge. Have them do the math to figure at least three different positions for their supports, making use of the limited lengths of the craft sticks.

You can use a high-adhesive tape, such as duct tape, or something similar to hold the bridges to the desks, and let the students observe how the different support positions affect the strength of the bridge. Discuss how the forces are being applied in vertical and horizontal directions, and how the result flows along the support beam, which is the hypotenuse of the right triangle. Invite them to investigate other support positions or even other bridge designs that might use the triangle theories in a different way.

This model can get the students into a creative mood, and can make solving parts of the Pythagorean theorem an automatic process for them. Once they've measured the length of the craft stick, they can begin to apply the theorem, as the other two sides of the triangle vary in length. They'll have their calculators out, and will have the square root button down pat before they're done. If the students are working in groups, make sure that all of the team members are getting a chance to work through the math, otherwise you'll get a couple of experts and a bunch of observers.

The Pythagorean theorem , which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, is a critical concept for middle and high school math students. Diagrams , which are drawings that illustrate the principles involved, and models , which are real-life scenarios that require the use of the learning principle, are useful in illustrating the mathematical principles involved with the Pythagorean theorem, and in inspiring the students to become adept at using them.

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- Uses of Pythagoras’ Theorem.
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## What Are Some Real Life Applications of the Pythagorean Theorem?

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