1. 4-8 The Pythagorean Theorem 0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems The Pythagorean Theorem

2. 4-8 The Pythagorean Theorem Warm Up Use a calculator to find each value. Round to the nearest hundredth. 1. 2. 3. 4. 5.48 3.74 7.42 6.93

3. 4-8 The Pythagorean Theorem  What is a formula?  When would you use a formula outside of school?  Carpenter- Building a house  Pharmacist- Measuring out liquid medicine  Other examples?

4. 4-8 The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

5. 4-8 The Pythagorean Theorem  On Your Paper, I would like for you to write what you remember from 7 th grade about the Pythagorean Theorem…any ideas?  After watching the video, any other ideas about the Pythagorean Theorem? http://www.youtube.com/watch?v=DRRVu -RHQWE&feature=related

6. 4-8 The Pythagorean Theorem  When I say right triangle, what does that mean? Pythagoras determined that if you know 2 sides of a right triangle, you can determine the other side

7. 4-8 The Pythagorean Theorem 4 5 c 6.40  c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c 2 4 2 + 5 2 = c 2 16 + 25 = c 2 41 = c Simplify powers. Solve for c; c = c 2. Additional Example 1A: Finding the Length of a Hypotenuse Find the length of the hypotenuse to the nearest hundredth. 41 = c 2

8. 4-8 The Pythagorean Theorem triangle with coordinates (–2, –2), (–2, 4), and (3, –2) ‏ x y The points form a right triangle. (–2, –2) ‏ (–2, 4) ‏ (3, –2) ‏ Check It Out: Example 1B 7.81  c Pythagorean Theorem a 2 + b 2 = c 2 6 2 + 5 2 = c 2 36 + 25 = c 2 61 = c Simplify powers. Solve for c; c = c 2. Substitute for a and b. Find the length of the hypotenuse to the nearest hundredth.

9. 4-8 The Pythagorean Theorem Additional Example 2: Finding the Length of a Leg in a Right Triangle 25 7 b Find the positive square root. b = 24 a 2 + b 2 = c 2 7 2 + b 2 = 25 2 49 + b 2 = 625 –49 b 2 = 576 Solve for the unknown side in the right triangle to the nearest tenth. Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 49 from each side.

10. 4-8 The Pythagorean Theorem  1 st step- draw your other 2 lines- that will give you a and b! a 2 + b 2 = c 2 4 2 + 7 2 = c 2 16 + 49 = c 2 65= c 2 8.1= c

11. 4-8 The Pythagorean Theorem  1 st step- draw your other 2 lines- that will give you a and b! a 2 + b 2 = c 2 3 2 + 8 2 = c 2 65 = c 2 8.5 = c

12. 4-8 The Pythagorean Theorem a 2 + b 2 = c 2 350 2 + 725 2 = c 2 122,500 + 525,625 = c 2 648,125 = c 2 805 ≈ c Find the positive square root. Substitute for a and b. Pythagorean Theorem The two planes are approximately 805 miles apart. Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land? Simplify powers. Add.

13. 4-8 The Pythagorean Theorem  You have just picked up a ground ball at 1 st base and you see the other team’s player running towards third base. How far do you have to throw the ball to get it from 1 st base to 3 rd base and throw the runner out? a 2 + b 2 = c 2 90 2 + 90 2 = c 2 8100 + 8100 =c 2 16200 = c 2 127.3 ≈ c

14. 4-8 The Pythagorean Theorem a 2 + b 2 = c 2 25 2 + 10 2 = c 2 625 + 100 =c 2 725 = c 2 26.9 ≈ c Find the positive square root. Substitute for a and b. Pythagorean Theorem You have locked yourself out of the house and the only open window is one the 2 nd floor, 25 feet above the ground. Because there is a bush by the window, you must place the ladder 10 feet away from the house. What length of ladder do you need? Simplify powers. Add.

15. 4-8 The Pythagorean Theorem Oscar’s dog house is shaped like a tent. The slanted sides are both 5 ft. long and the bottom of the house is 6 ft across. What is the height of his dog house, at its tallest point.

16. 4-8 The Pythagorean Theorem 1. Identify the height of the triangle. A. 14 m B. 15 m C. 16 m D. 17 m Lesson Quiz for Student Response Systems

17. 4-8 The Pythagorean Theorem 2. Identify the length of side c to the nearest meter. A. 9 m B. 10 m C. 11 m D. 12 m Lesson Quiz for Student Response Systems