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Pythagorean Theorem. Pythagorean theorem: The Pythagorean Theorem, a²+b²=c² , is used to find the length of any SIDE of a RIGHT triangle. Label the sides of the triangle. a and b are called the Legs .
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Pythagorean theorem: • The Pythagorean Theorem, a²+b²=c², is used to find the length of any SIDE of a RIGHTtriangle. • Label the sides of the triangle. • a and b are called the Legs. • Notice: The two Legsalways form a “L” shape at the right angle of the triangle. • Side “c” is called the hypotenuse. • The hypotenuse is always located directly across from the right side. • The hypotenuse, “c” will always be the side with the longest length. c a Hypotenuse b LEGS
Example 1: c² = a² + b² c² = 82 + 62 c² = 64 + 36 8 ft X c² = 100 √c² = √100 6 ft. c = 10
Example 2: You can write the formula asa² + b² = c2 or c2 = a² + b² a² + b² = c2 34² + 15² = c2 1381 = c² √1381 = √c² 37.16 = c X 34 cm 15 cm
Example 3: c² = a² + b² 10² = a² + 4² 10 in X 100 = a² + 16 -16 = - 16 4 in. 84 = a² √84 = √a² a = 2 √ 21 or 9.17
Example 4: (Your Turn) c² = a² + b² 15 15² = 6²+ b² 225 = 36 + b² √189 = √b² √189 = b 3√21 or 13.75=b 6 X
Example 5: Determine whether each triangle with sides of given length is a right triangle. A) 1, 7, 4 7² = 1² + 4² 49 = 1 + 16 49 > 17 No. It is not a right triangle. It is an obtuse triangle, because “c2 “ is greater than the square of the legs! B) 10, 8, 6 10² = 8² + 6² 100 = 64 + 36 100 = 100 Yes. It is a right triangle, because c2 = a2 + b2 !
