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Vocabulary
Pythagorean triple
A set of three integers that satisfy the Pythagorean Theorem
3 – 4 – 5
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
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
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