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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 5-2b. Objective. Solve problems using the Pythagorean Theorem. Example 5-2b. Vocabulary. Pythagorean triple. A set of three integers that satisfy the Pythagorean Theorem

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

  2. Splash Screen

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

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

  5. Example 5-2b Pythagorean triple

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

  7. Example 5-1a RAMPSA 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. b 1/2

  8. 24.12 = 22 + b2 b Write the Pythagorean Theorem formula Replace c with 24.1 Replace a with 2 Bring down b 1/2

  9. Follow order of operations P E MD AS Solve all exponents 24.12 = 22 + b2 Ask: “What is being done to the variable?” 580.81 = 4 + b2 Variable is being added by 4 580.81 - 4 = 4 - 4 + b2 Do the inverse on both sides of the = sign b2 576.81 = Subtract on each side of the = sign 1/2

  10. Ask: “What is being done to the variable?” Variable is being squared 24.12 = 22 + b2 Do the inverse on both sides of the = sign 580.81 = 4 + b2 580.81 - 4 = 4 - 4 + b2 Find square root of both sides 576.81 = b2 Add dimensional analysis 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? b2 24.02 = b Answer: End of ramp = 24 feet from the entrance 1/2

  11. Example 5-1b RAMPSIf 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

  12. Example 5-2a Multiply the triple 5-12-13 by the numbers 2, 3, 4, 5, and 10 to find more Pythagorean triples. 169 =25 + 144 169 = 169 10 26 24 676=100 + 576 676 = 676 15 36 39 1521 = 225 + 1296 1521 = 1521 20 48 52 2704 =400 + 2304 2704 = 2704 25 60 65 4225 = 625 + 3600 4225 = 4225 130 16,900 = 16,900 500 120 16,900 =2,500+14,400 2/2

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

  14. Example 5-2b * Multiply the triple 8-15-17 by the numbers 2, 3, 4, and 10 to find more Pythagorean triples. 2/2

  15. End of Lesson 5 Assignment

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