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The Pythagorean Theorem Objectives • The objective of this lesson is for you to learn and apply the Pythagorean Theorem -- an important relationship between the three sides of a right triangle. The Theorem • One of the most important and fundamental theorems in all of mathematics • Where a and b are the two legs of the right triangle and c is the hypotenuse. Sample Problem • If the two legs of a right triangle measure 3 and 6, then what is the length of the hypotenuse? Basic Problems • If the two legs of a right triangle measure 5 and 12, then what is the length of the hypotenuse? • If the hypotenuse of a right triangle measures 10 and one leg measures 5, then what is the length of the other leg? Problems • Find out the length of sides a and b on the following triangle: Problems • What is the longest straight pole, like the red one, that you can have inside the box? Application Problems • There is a building with a 12 ft high window. You want to use a ladder to go up to the window, and you decide to keep the ladder 5 ft away from the building to have a good slant. How long should the ladder be? • On a baseball diamond the bases are 90 ft apart. What is the distance from home plate to second base in a straight line? Pythagorean Triples • Pythagorean Triples are sets of three integer values that satisfy the Pythagorean Theorem • Common Triples ( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16,63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)