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Objective

Solve problems using the Pythagorean Theorem

Vocabulary

Pythagorean triple

A set of three integers that satisfy the Pythagorean Theorem

3 – 4 – 5

Pythagorean triple

A B C C2 = a2 + b2 Solution Check

Original 3 4 5 25 =9 + 16 25 = 25

2

3

4

10

Example 1 Use the Pythagorean Theorem

Example 2 Write Pythagorean Triples

RAMPS A ramp to the entrance of a newly constructed building must be built according to accessibility guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the end of the ramp from the entrance?

Notice the problem involves a right triangle.

Use the Pythagorean Theorem.

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b

1/2

Write the Pythagorean Theorem formula

Replace c with 24.1

24.12

Replace a with 2

b

Bring down b

= 22 + b2

1/2

24.12 = 22 + b2

Follow order of operationsP E MD AS

Solve all exponents

580.81 = 4 + b2

Ask: “What is being done to the variable?”

Variable is being added by 4

Do the inverse on both sides of the = sign

580.81 - 4 = 4 - 4 + b2

Subtract on each side of the = sign576.81 = b2

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24.12 = 22 + b2

580.81 = 4 + b2

580.81 - 4 = 4 - 4 + b2

576.81 = b2

Ask: “What is being done to the variable?”

Variable is being squared

Do the inverse on both sides of the = sign

b2

Find square root of both sides

24.02 = b

Add dimensional analysis

Answer: End of ramp = 24 feet from the entrance

If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the end of the ramp from the entrance?

RAMPS If a truck ramp is 32 feet long and the top of the ramp is 10 feet off the ground, how far is the end of the ramp from the truck?

Answer: End of ramp = 30.40 feet from truck

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Multiply the triple 5-12-13 by the numbers 2, 3, 4, 5, and 10 to find more Pythagorean triples.

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A B C C2 = a2 + b2 Solution Check

Original 5 12 13

2

3

4

5

10

169 =25 + 144 169 = 169

10

15

20

25

500

24

36

48

60

120

26

39

52

65

130

676=100 + 576

1521 = 225 + 1296

2704 =400 + 2304

4225 = 625 + 3600

16,900 =2,500+14,400

676 = 676

1521 = 1521

2704 = 2704

4225 = 4225

16,900 = 16,900

Answer: 10, 24, 26;

15, 36, 39;

20, 48, 52;

25, 60, 65;

50, 120, 130

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Multiply the triple 8-15-17 by the numbers 2, 3, 4, and 10 to find more Pythagorean triples.

*

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A B C C2 = a2 + b2 Solution Check

Original 8 15 17

2 16 30 34

3 24 45 51

4 32 60 68

10 80 150 170

Assignment

Lesson 3:5Using the Pythagorean

Theorem4 - 17 All