8.2. Applications of 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^2Example B
Find the distance between (1, 5) and (5, 2).
MakeA( 1 , 5 )andB( 5 , 2 ). Plug into the distance formula.
d=√
( 1 − 5 )^2 +( 5 − 2 )^2
=
√
(− 4 )^2 +( 3 )^2
=
√
16 + 9 =
√
25 = 5
You might recall that the distance formula was presented asd=
√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2 , with the first and second
points switched. It does not matter which point is first as long asxandyare both first in each parenthesis. In
Example 7, we could have switchedAandBand would still get the same answer.
d=√
( 5 − 1 )^2 +( 2 − 5 )^2
=
√
( 4 )^2 +(− 3 )^2
=
√
16 + 9 =
√
25 = 5
Also, just like the lengths of the sides of a triangle, distances are always positive.
Example C
Determine if the following triangles are acute, right or obtuse.
a)
b)
Set the shorter sides in each triangle equal toaandband the longest side equal toc.
a)
62 +( 3