EXAMPLE 3.7.1

Find the missing side length for each triangle shown below.

SOLUTIONS

1. According to the Pythagorean Theorem:

C squared equals 8 squared plus 5 squared.
C squared equals 64 plus 25.
C squared equals 89
C equals the square root of 89.
C is approximately equal to 9.43 inches.

Note that C is not a whole number. This is not an unusual result when we use the Pythagorean Theorem.

 

2. In this case, in order to use the Pythagorean Theorem correctly we must realize that x represents the length of a leg, not the hypotenuse.

20 squared equals 16 squared plus x squared.
400 equals 256 plus x squared.
400 minus 256 equals x squared.
144 equals x squared.
x equals the square root of 144.
x equals 12 centimeters.