Real World Application of the Pythagorean Theorem
Real World Application of the 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
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 HD TV. 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 HD TV 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 must now decide which TV they really want, because their prediction was wrong.
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