Basic Mathematics for College Students

c. What side is the shorter

leg?

10. What is the first step when solving the equation
    for?

NOTATION

Complete the solution to solve the equation, where and

.

11.

12.

a

a 1

a^2 

a^2  225   289 

a^2  

a^2  152  172

10 c

1 c

c^2

 36 c^2

82  62 c^2

c 0

a 0

25 b^2  81 b

C

B A

30°

60°

9.4 The Pythagorean Theorem 751

SolutionWe must substitute the longest side length, 11, for ,because it is the Now TryProblem 39
possible hypotenuse. The lengths of 6 and 8 may be substituted for either or.

This is the Pythagorean equation.

Substitute 6 for a,8 for b,and 11 for c.

Evaluate each exponential expression.

This is a false statement.

Since 100  121 , the triangle is not a right triangle.

100  121

36  64  121

62  82  112

a^2 b^2 c^2

a b

c

1.13 ft 2.no 3.56 in. 4. 124 m4.90 m 5.yes

ANSWERS TO SELF CHECKS

SECTION 9.4 STUDY SET

VOCABULARY

Fill in the blanks.

1. In a right triangle, the side opposite the 90° angle is
   called the. The other two sides are called
   .


2. The Pythagorean theorem is named after the Greek
   mathematician, , who is thought to have
   been the first to prove it.


3. The theorem states that in any right
   triangle, the square of the length of the hypotenuse is
   equal to the sum of the squares of the lengths of the
   two legs.


4. is called the Pythagorean.

CONCEPTS

Fill in the blanks.

5. If and are the lengths of two legs of a right
   triangle and is the length of the hypotenuse,
   then .


6. The two solutions of are  or .
   If represents the length of the hypotenuse of a right
   triangle, then we can discard the solution.


7. The converse of the Pythagorean theorem: If a
   triangle has three sides of lengths ,,and ,such
   that , then the triangle is a
   triangle.


8. Use a protractor to draw an example of a right
   triangle.

a^2 b^2 c^2

ab c

c

c^2  36 c c

c

a b

a^2 b^2 c^2

9. Refer to the triangle on the right.
   a. What side is the hypotenuse?
   b. What side is the longer leg?

3

1

6

 64

100