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Transparency 5 Click the mouse button or press the Space Bar to display the answers.

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Example 5-2b Objective Solve problems using the Pythagorean Theorem

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Example 5-2b Vocabulary Pythagorean triple A set of three integers that satisfy the Pythagorean Theorem 3 – 4 – 5

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Example 5-2b Pythagorean triple ABCC 2 = a 2 + b 2 Solution Check Original34525 =9 + 1625 = 25 2 3 4 10

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Lesson 5 Contents Example 1Use the Pythagorean Theorem Example 2Write Pythagorean Triples

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Example 5-1a 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. 1/2 b

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Write the Pythagorean Theorem formula Replace c with 24.1 24.1 2 Replace a with 2 b Bring down b = 2 2 + b 2

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1/2 24.1 2 = 2 2 + b 2 Follow order of operations P E MD AS Solve all exponents 580.81 = 4 + b 2 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+ b 2 Subtract on each side of the = sign 576.81 = b 2

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1/2 24.1 2 = 2 2 + b 2 580.81= 4+ b 2 580.81 - 4 = 4 - 4 + b 2 576.81 = b 2 Ask: “What is being done to the variable?” Variable is being squared Do the inverse on both sides of the = sign b2b2 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?

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Example 5-1b 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 1/2

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Example 5-2a Multiply the triple 5-12-13 by the numbers 2, 3, 4, 5, and 10 to find more Pythagorean triples. 2/2 ABCC 2 = a 2 + b 2 Solution Check Original51213 2 3 4 5 10 169 =25 + 144169 = 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

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Example 5-2a Answer: 10, 24, 26; 15, 36, 39; 20, 48, 52; 25, 60, 65; 50, 120, 130 2/2

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Example 5-2b Multiply the triple 8-15-17 by the numbers 2, 3, 4, and 10 to find more Pythagorean triples. * 2/2 ABCC 2 = a 2 + b 2 Solution Check Original81517 2 163034 3 244551 4 326068 10 80150170

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End of Lesson 5 Assignment Lesson 3:5 Using the Pythagorean Theorem 4 - 17 All

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