Everyday Word Problems for the Pythagorean Theorem

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One way to familiarize yourself with the Pythagorean theorem is through the use of simple, every day word problems. Learn about every day word problems for the Pythagorean theorem with help from an experienced math tutor in this free video clip.

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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to talk about every day word problems for the Pythagorean theorem. So most Pythagorean theorem word problems are going to deal with some sort of leaning ladder somewhere. So we can take a building and we're going to lean the ladder against it and you can give the students one of three information pieces. So you can tell them the distance that the ladder is from the building, the base of the ladder, the foot of the ladder from the building. And you always want to kind of talk about the foot of the ladder because sometimes they don't know what that means. So if you give them the distance between the foot of the ladder and the building. You say that distance six feet, and let's say that you tell them that the distance from the ladder to the top of the building is ten feet and your question then would be "How tall is this building?" If the ladder reaches the top it at ten feet and I'm six feet away. How tall is this? That's your x. They have to recognize that the building is going to form a 90 degree angle with the floor because they're perpendicular. And then they have to see that they are obviously using the Pythagorean theorem. Now you have to realize what you're given. Well I'm given the diagonal, I'm given the ladder to the building, which is my hypotenuse. So for c I'm going to substitute ten squared. And then I'm given one of the legs, and it doesn't matter which one of these I plug in, so I'll plug it in for b and I'm going to put six squared plus a squared. And now I'm going to go ahead and simplify a squared plus 36 equals 100. And then I get a squared equals 64 after I subtract 36 from both sides and then when I square root each side, I'm going to get a equals eight, so I know that my building is eight feet tall. My name is Marija and I just gave you an every day word problem to use with the Pythagorean theorem.


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