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Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)

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Pythagorean Relationship a 2 + b 2 = c 2 a c b b Area = b 2 Area = a 2 a c Area = c 2

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Applying the Pythagorean Relationship We know that: a 2 + b 2 = c 2 a b c

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Applying the Pythagorean Relationship a b c Using this… If we know the lengths of ANY two sides of a right angle triangle, we can use the Pythagorean Relationship to find the length of the unknown side.

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Applying the Pythagorean Relationship a b c Situation Two: We know the lengths of the hypotenuse (c) and one leg (b) of a right angle triangle. How can we find the length of the other leg (a)?

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Applying the Pythagorean Relationship a b c Since we know that: a 2 + b 2 = c 2 Then: a 2 = c 2 - b 2

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Applying the Pythagorean Relationship a b c Since: a 2 = c 2 - b 2 Then: a = (c 2 - b 2 )

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Applying the Pythagorean Relationship a = ? b = 5m c = 9 Example: c = 9m; b = 5m a = (c 2 - b 2 ) a = (9 2 - 5 2 ) a = (81 - 25) a = 56 a = 7.5 m

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Problem a = ? b = 6.2cm c = 8.5cm Find the length of the unknown side (a).

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Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

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