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

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

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

4. 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.

5. 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)?

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

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

8. 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

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