8.2. Applications of the Pythagorean Theorem http://www.ck12.org
8.2 Applications of the Pythagorean Theorem
Here you’ll learn several applications of the Pythagorean Theorem.
What if you had a 52" High Definition Television (52" being the length of the diagonal of the rectangular viewing
area)? High Definition Televisions (HDTVs) have sides in the ratio of 16:9. What is the length and width of a 52”
HDTV? What is the length and width of an HDTV with aylong diagonal?
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Click image to the left for more content.CK-12 Foundation: Chapter8ApplicationsofthePythagoreanTheoremA
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Click image to the left for more content.James Sousa:PythagoreanTheoremandItsConverse
Guidance
There are many different applications of the Pythagorean Theorem. Three applications are explored below.
Find the Height of an Isosceles Triangle
One way to use The Pythagorean Theorem is to identify the heights in isosceles triangles so you can calculate the
area. The area of a triangle is^12 bh, wherebis the base andhis the height (or altitude).
If you are given the base and the sides of an isosceles triangle, you can use the Pythagorean Theorem to calculate
the height.
Prove the Distance Formula
Another application of the Pythagorean Theorem is the Distance Formula.
First, draw the vertical and horizontal lengths to make a right triangle. Then, use the differences to find these
distances.
Now that we have a right triangle, we can use the Pythagorean Theorem to findd.