8.1. The Pythagorean Theorem http://www.ck12.org
72 +h^2 = 92
49 +h^2 = 81
h^2 = 32
h=√
32 = 4
√
2
Now, usehandbin the formula for the area of a triangle.
A=
1
2
bh=1
2
( 14 )
(
4
√
2
)
= 28
√
2 units^2The Distance Formula
Another application of the Pythagorean Theorem is the Distance Formula. We have already been using the Distance
Formula in this text, but we can prove it here.
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.