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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 3 – 4 – 5

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

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

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

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

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

1/ = b = 4+ b = b = 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?

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 = feet from truck 1/2

Example 5-2a Multiply the triple 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  = = = = = = ,900 =2,500+14, = = = = ,900 = 16,900

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

Example 5-2b Multiply the triple by the numbers 2, 3, 4, and 10 to find more Pythagorean triples. * 2/2 ABCC 2 = a 2 + b 2 Solution Check Original81517    

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