10-5 The Pythagorean Theorem
Find each missing length. If necessary, round to the nearest hundredth.
1. SOLUTION: Use the Pythagorean Theorem, substituting 3 for a and 4 for b.
2. SOLUTION: Use the Pythagorean Theorem, substituting 4 for a and 21 for c.
3. SOLUTION: Use the Pythagorean Theorem, substituting 6 for b and 19 for c.
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10-5 The Pythagorean Theorem
3. SOLUTION: Use the Pythagorean Theorem, substituting 6 for b and 19 for c.
4. SOLUTION: Use the Pythagorean Theorem, substituting 8 for a and 12 for b.
5. BASEBALL A baseball diamond is a square. The distance between consecutive bases is 90 feet.
a. How far does a catcher have to throw the ball from home plate to second base?
b. How far does a third baseman throw the ball to the first baseman from a point in the baseline 15 feet from third
to second base?
c. A base runner going from first to second base is 100 feet from home plate. How far is the runner from second
base?
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SOLUTION: a. Use the Pythagorean Theorem, substituting 90 for a and 90 for b.
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a. How far does a catcher have to throw the ball from home plate to second base?
b. How far does a third baseman throw the ball to the first baseman from a point in the baseline 15 feet from third
second
base?
10-5toThe
Pythagorean
Theorem
c. A base runner going from first to second base is 100 feet from home plate. How far is the runner from second
base?
SOLUTION: a. Use the Pythagorean Theorem, substituting 90 for a and 90 for b.
The catcher has to throw the ball about 127 ft from home plate to second base.
b. The diagram below illustrates the throw made by the third baseman.
The length of a is 90 – 15 or 75 feet. Find the length of the throw c by using the Pythagorean Theorem,
substituting 75 for a and 90 for b.
The third baseman has to throw the ball about 117 feet to the first baseman.
c. The diagram below illustrates the position of the base runner.
Use the Pythagorean Theorem to find the length of side a by substituting 90 for b and 100 for c.
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10-5 The Pythagorean Theorem
Use the Pythagorean Theorem to find the length of side a by substituting 90 for b and 100 for c.
So, the base runner is about 44 feet from first base to second base. Therefore, the distance the base runner is from
second is about 90 – 44 or 46 feet.
Determine whether each set of measures can be the lengths of the sides of a right triangle.
6. 8, 12, 16
SOLUTION: 2
2
2
Since the measure of the longest side is 16, let c = 16, a = 8, and b = 12. Then determine whether c = a + b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths 8, 12, and 16 is not a right triangle.
7. 28, 45, 53
SOLUTION: 2
2
2
Since the measure of the longest side is 53, let c = 53, a = 28, and b = 45. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 28, 45, and 53 is a right triangle.
8. 7, 24, 25
SOLUTION: 2
2
2
Since the measure of the longest side is 25, let c = 25, a = 7, and b = 24. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 7, 24, and 25 is a right triangle.
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9. 15, 25,
Page 4
SOLUTION: 2
2
2
10-5 The Pythagorean Theorem
2
2
2
Yes, because c = a + b , a triangle with side lengths 7, 24, and 25 is a right triangle.
9. 15, 25, 45
SOLUTION: 2
2
2
Since the measure of the longest side is 45, let c = 45, a = 15, and b = 25. Then determine whether c = a + b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths 15, 25, and 45 is not a right triangle.
Find each missing length. If necessary, round to the nearest hundredth.
10. SOLUTION: Use the Pythagorean Theorem, substituting 6 for a and 14 for b.
11. SOLUTION: Use the Pythagorean Theorem, substituting 2 for a and 12 for c.
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12. SOLUTION: Page 5
10-5 The Pythagorean Theorem
12. SOLUTION: Use the Pythagorean Theorem, substituting
for a and 20 for b.
13. SOLUTION: Use the Pythagorean Theorem, substituting 9 for b and 31 for c.
14. SOLUTION: Use the Pythagorean Theorem, substituting 16 for a and 26 for c.
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10-5 The Pythagorean Theorem
14. SOLUTION: Use the Pythagorean Theorem, substituting 16 for a and 26 for c.
15. SOLUTION: Use the Pythagorean Theorem, substituting
for a and
for b.
16. SOLUTION: Use the Pythagorean Theorem, substituting 7 for b and 25 for c.
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10-5 The Pythagorean Theorem
16. SOLUTION: Use the Pythagorean Theorem, substituting 7 for b and 25 for c.
17. SOLUTION: Use the Pythagorean Theorem, substituting 5 for a and
for c.
18. SOLUTION: Use the Pythagorean Theorem, substituting
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for b and
for c.
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10-5 The Pythagorean Theorem
18. SOLUTION: Use the Pythagorean Theorem, substituting
for b and
for c.
19. TELEVISION Larry is buying an entertainment stand for his television. The diagonal of his television is 42 inches.
The space for the television measures 30 inches by 36 inches. Will Larry’s television fit? Explain.
SOLUTION: Use the Pythagorean Theorem, substituting 30 for a and 36 for b.
Yes; sample answer: The diagonal of the space in the TV stand is about 46.9 inches, which is greater than the
diagonal of the television, so Larry’s TV will fit.
Determine whether each set of measures can be the lengths of the sides of a right triangle. Then
determine whether they form a Pythagorean triple.
20. 9, 40, 41
SOLUTION: 2
2
2
Since the measure of the longest side is 41, let c = 41, a = 9, and b = 40. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 9, 40, and 41 is a right triangle.
2
2
2
Yes, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
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21. Page 9
answer:Theorem
The diagonal of the space in the TV stand is about 46.9 inches, which is greater than the
10-5Yes;
The sample
Pythagorean
diagonal of the television, so Larry’s TV will fit.
Determine whether each set of measures can be the lengths of the sides of a right triangle. Then
determine whether they form a Pythagorean triple.
20. 9, 40, 41
SOLUTION: 2
2
2
Since the measure of the longest side is 41, let c = 41, a = 9, and b = 40. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 9, 40, and 41 is a right triangle.
2
2
2
Yes, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
21. SOLUTION: Since the measure of the longest side is
, let c =
, a = 3, and b =
2
2
. Then determine whether c = a +
2
b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths 3,
, and
is not a right triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
22. SOLUTION: Since the measure of the longest side is 12, let c = 12, a = 4, and b =
2
2
2
No, because c ≠ a + b , a triangle with side lengths 4,
2
2
2
. Then determine whether c = a + b .
, and 12 is not a right triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
23. SOLUTION: eSolutions Manual - Powered by Cognero
Since the measure of the longest side is 14, let c = 14, a =
2
2
2Page 10
, and b = 7. Then determine whether c = a + b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths 4,
, and 12 is not a right triangle.
2
2
2
a Pythagorean
triple is a group of three whole numbers that satisfy the equation c = a + b , where c
10-5No,
Thebecause
Pythagorean
Theorem
is the greatest number.
23. SOLUTION: 2
Since the measure of the longest side is 14, let c = 14, a =
2
2
2
No, because c ≠ a + b , a triangle with side lengths
2
2
, and b = 7. Then determine whether c = a + b .
, 7, and 14 is not a right triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
24. 8, 31.5, 32.5
SOLUTION: 2
2
2
Since the measure of the longest side is 32.5, let c = 32.5, a = 8, and b = 31.5. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 8, 31.5, and 32.5 is a right triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number, but b and c are not whole numbers.
25. SOLUTION: Since the measure of the longest side is
2
, let c =
,a =
, and b =
2
. Then determine whether c =
2
a +b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths
,
, and
is not a right triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
26. 18, 24, 30
SOLUTION: 2
2
2
Since the measure of the longest side is 30, let c = 30, a = 18, and b = 24. Then determine whether c = a + b .
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2
2
2
No, because c ≠ a + b , a triangle with side lengths
,
, and
is not a right triangle.
2
2
2
10-5No,
Thebecause
Pythagorean
Theorem
a Pythagorean
triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
26. 18, 24, 30
SOLUTION: 2
2
2
2
2
2
2
Since the measure of the longest side is 30, let c = 30, a = 18, and b = 24. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 18, 24, and 30 is a right triangle.
2
Yes, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
27. 36, 77, 85
SOLUTION: 2
Since the measure of the longest side is 85, let c = 85, a = 36, and b = 77. Then determine whether c = a + b .
2
2
2
Yes, because c = a + b , a triangle with side lengths 36, 77, and 85 is a right triangle.
2
2
2
Yes, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
28. 17, 33, 98
SOLUTION: Since the measure of the longest side is 98, let c = 98, a = 17, and b = 33. The length of c is greater than the sum of
a and b, so this is not a triangle. 2
2
2
No, because c ≠ a + b , a triangle with side lengths 17, 33, and 98 is not a triangle.
2
2
2
No, because a Pythagorean triple is a group of three whole numbers that satisfy the equation c = a + b , where c
is the greatest number.
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