Pre-Algebra Chapter 9

Concept Check
Which side of a right triangle is the hypotenuse?
If you know the lengths of two sides of a right triangle, you can use the
Pythagorean Theorem to find the length of the third side. This is called
solving a right triangle.
Example 2
Solve a Right Triangle
Find the length of the leg of the right triangle.
c 2 a 2 b 2
Pythagorean Theorem
14 2 a 2 10 2 Replace c with 14 and b with 10.
196 a 2 100 Evaluate 14 2 and 10 2 .
196 – 100 a 2 100 – 100 Subtract 100 from each side.
96 a 2 Simplify.
96 a 2
Take the square root of each side.
2nd
[] 96 ENTER 9.797958971
The length of the leg is about 9.8 centimeters.
a cm
14 cm
10 cm
Standardized tests often contain questions involving the Pythagorean
Theorem.
Standardized
Test Practice
Example 3
Multiple-Choice Test Item
Use the Pythagorean Theorem
A painter positions a 20-foot ladder against a house so that the
base of the ladder is 4 feet from the house. About how high does
the ladder reach on the side of the house?
A 17.9 ft B 18.0 ft C 19.6 ft D 20.4 ft
Test-Taking Tip
To help visualize the
problem, it may be helpful
to draw a diagram that
represents the situation.
Read the Test Item
Make a drawing to illustrate the problem.
The ladder, ground, and side of the house
form a right triangle.
20 ft
Solve the Test Item
Use the Pythagorean Theorem to find how
high the ladder reaches on the side of the house.
c 2 a 2 b 2 Pythagorean Theorem
20 2 4 2 b 2 Replace c with 20 and a with 4.
400 16 b 2 Evaluate 20 2 and 4 2 .
400 16 16 b 2 16 Subtract 16 from each side.
384 b 2 Simplify.
384 b
2
Take the square root of each side.
19.6 b Round to the nearest tenth.
The ladder reaches about 19.6 feet on the side of the house.
The answer is C.
4 ft
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Lesson 9-5 The Pythagorean Theorem 461