1. Pythagorean Theorem SOL 8.10 cont.

2. Review Previously, we used the Pythagorean Theorem to find the hypotenuse of a right triangle. (a 2 + b 2 = c 2 ) We were given a and b and found c! What happens if we are given one of the legs and the hypotenuse, and are asked to find the measurement for the second leg? If we are given a and c, or b and c, we can find the missing leg!

3. Example 3 Solve for a. a 2 + b 2 = c 2 a 2 + 6 2 = 15 2 a 2 + 36 = 225 - 36 -36 a 2 = 189 √a 2 = √189 a = 13.7 15 a 6

4. Example 4 Solve for b. a 2 + b 2 = c 2 7 2 + b 2 = 16 2 49 + b 2 = 256 -49 b 2 = 207 √b 2 = √207 b = 14.4 7 b 16

5. Your Turn! Use the Pythagorean Theorem to solve. Round to the nearest tenth, if necessary. 1. b = 9, c = 12 7.9 2. a = 3, c = 8 7.4 3. a = 15, b = 18 23.4

6. Pythagorean Triple A Pythagorean Triple is three positive integers, a, b, and c, where a 2 + b 2 = c 2. Example: 3, 4, 5 3 2 + 4 2 = 5 2 9 + 16 = 2525 = 25 Example: 5, 12, 13 5 2 + 12 2 = 13 2 25 + 144 = 169169 = 169 3 4 55 12 137 24 25 6 8 1010 24 2614 48 50 9 12 1515 36 3921 72 75 12 16 2020 48 5228 96 100

7. Identifying a Right Triangle! A triangle is a right triangle if the sides of a triangle have lengths a, b, and c such that a 2 + b 2 = c 2. (Hint: remember c is always the longest side.) Ex: The measures of three sides of a triangle are 15 inches, 8 inches, and 17 inches. Determine whether the triangle is a right triangle. 15 2 + 8 2 = 17 2 225 + 64 = 289 289 = 289 since they are equal the triangle must be a right triangle

8. Your Turn! Determine if the following sides make a right triangle by using the Pythagorean Theorem? 1. 18, 24, and 30 Yes (900 = 900) 2. 4, 7, and 5 No (41 ≠ 49)

9. Tonight’s Homework! Solve. Round to the nearest tenth, if necessary! Determine if the following are right triangles? Show your work! 1. b = 15, c = 25 2. a = 10, c = 25 3. b = 14, c = 20 4. b = 17, c = 20 5. a = 3, c = 8 6. b = 3.4, c = 8.6 7. a = 15, b = 18 1. 9, 40, 41 2. 45, 26, 53 3. 1.6, 6.5, 6.3

10. Answers to HW 1. 20 2. 22.9 3. 14.3 4. 10.5 5. 7.4 6. 7.9 7. 23.4 1. Yes (1681 = 1681) 2. No (2701 = 2809) 3. Yes (42.25 = 42.25)