Pythagorean Theorem - Real World Application
Posted by David Wetzel
Pythagorean Theorem
The Pythagorean Theorem is used any time you have a right triangle in which you know the length of two sides and want to find the third side.
The formula is: a2 + b2 = c2
There are many strategies for getting students to learn how to solve a problem related to this theorem. Many of these problems are boring, procedural driven, and lacking in connection to real world applications.
In the view of many this is often necessary because they do not have the time to teach it any other way. Curriculum, testing, and No Child Left Behind pressures cause these views.
However, there are other strategies to teach the same concept and yet make it more interesting for students. The critical aspect of this strategy is to make connections to their world.
Students always ask:
- When will I every use the Pythagorean Theorem?
- Why do need to learn this? It is boring!
The answer is, in any kind of job that deals with triangles. For example, carpenters, engineers, architects, construction workers, those who measure and mark land, artists, and designers of many sorts need to know it.
Problem Solving Application
The following are problem is more interesting and designed to find the length of a2 and b2, when only c2 is known.
Shopping for a New TV
Jacob and Denise, brother and sister, are trying to get their parents to buy them a new TV. Their parents have agreed; however, they are limited to a size 32 inch TV.
Now they must go shopping to find the one they want. At their local electronics store, they discover that 42 inch TVs come in a lot shapes and sizes.
This does not seem to make since, until the salesman tells that 42 inches is diagonal measurement that is the normal way of sizing TVs.
They decide to compare the difference between a 32 inch standard TV and 32 inch flat screen HDTV. Jacob and Denise both agreed that they should buy the TV with greatest viewing area.
After looking a both TV types, they predicted that the flat screen HD TV had the greatest viewing area.
How would you determine which TV has the greatest viewing area?
Answer
TV Problem: the key to this problem is the aspect ratio of the TVs. The Standard TV has an aspect ratio of 4:3, while the Flat Screen HDTV has an aspect ratio of 21:9.
First they must find out what each unit equals (for example in the Standard TV is 4 units wide and 3 units high - aspect ration 4:3) in the aspect ratio for each TV by using the Pythagorean Theorem.
Next they must find the area of each TV using A = w x h.
Standard TV Area = 491.56 in2
Flat Screen HD TV Area = 370.44 in2
Jacob and Denise now must decide which TV they really want, because their prediction was wrong.
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This problem not only makes connections to something that students are actually interested in, they also make connections to other math concepts. Pythagorean Theorem now has a real world application to students and they will see its value.
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