2. The Pythagorean Theorem Algebra 1 Mrs. McGowan Grand Canyon University TEC 55 1

3. Learning Objectives Today you will learn to apply the Pythagorean Theorem. You will know you know this when you can find a side length of a right triangle given the lengths of its other two sides, with 85% accuracy, and apply the Pythagorean Theorem to real-world problems with 80% accuracy.

4. The Pythagorean Theorem Knowing how to apply the Pythagorean Theorem is an important skill in algebra. You will find that there are many real world applications to these skills that you might not have thought about. The Pythagorean Theorem is one of the most significant theorems in mathematics. To apply the theorem, you will need to use your knowledge of squares and square roots.

5. A Video on the Pythagorean Theorem (2007)

6. Using the Pythagorean Theorem to Find the Missing Hypothenus Use the Pythagorean Theorem to find the length of side c. a 2 + b 2 = c 2 3 2 + 4 2 = c 2 Plug values into the formula 9 + 16 = c 2 Simplify the squared values 25 = c 2 Simplify (add 9 and 16) 5 = c Take the square root of both sides of the equation (2004)

7. Using the Pythagorean Theorem to Find the Missing Leg a 2 + b 2 = c 2 a 2 + 6 2 = 10 2 Plug values into the formula a 2 + 36 = 100 Simplify the squared values a 2 + 36 = 100 Simplify (subtract 36 from both sides) a 2 = 64 a = 8 Take the square root of both sides of the equation (2004)

8. Solving a Real-World Pythagorean Theorem Problem a 2 + b 2 = c 2 15 2 + 20 2 = c 2 Plug values into the formula 225 + 400 = c 2 Simplify the squared values 625 = c 2 Simplify (add 225 and 400) 25 = c Take the square root of both sides of the equation Your boat is traveling due north at 20 miles per hour. A friend’s boat left at the same time from the same location and headed due west at 15 miles per hour. After an hour you get a call from your friend who tells you that he has just stopped because of engine trouble. How far must you travel to reach your friend? (2004)

9. Independent Practice Solve for y. X = 20 X = 11 (2004)

10. Independent Practice Solve for x. X = 3.46 X = 4.47 (2004)

11. Independent Practice - A baseball diamond is a square with sides of 90 feet. To the nearest foot, how long is a throw from third base to first base? X = 127. 28 X = 124.25 (2004)

12. Independent Practice A garden in the shape of a right triangle is represented by the figure at right. What is the length of the third side of the garden? 17.20 ft9.8 ft (2004)

13. References Ellis, W., Hollowell, K. A., Kennedy, P. A., Schultz, J. E. (2004). Holt Algebra 1. New York, New York: Holt, Rinehart, and Winston, Inc. ModuMath. (2007). Algebra: Pythagorean Theorem and Other Formulas [Full Video]. Available from http://www.discoveryeducation.com/

14. Correct!! Next Problem

15. Incorrect a 2 + b 2 = c 2 16 2 + 12 2 = c 2 Plug values into the formula 256 + 144 = c 2 Simplify the squared values 400 = c 2 Simplify (add 256 and 144) 20 = c Take the square root of both sides of the equation Next Problem

16. Correct!! Next Problem

17. Incorrect Next Problem a 2 + b 2 = c 2 2 2 + b 2 = 4 2 Plug values into the formula 4 + b 2 = 16 Simplify the squared values b 2 = 12 Simplify (subtract 4 from both sides) 3.46 = c Take the square root of both sides of the equation

18. Correct!! Next Problem

19. Incorrect Next Problem a 2 + b 2 = c 2 90 2 + 90 2 = c 2 Plug values into the formula 8100 + 8100 = c 2 Simplify the squared values 16200 = c 2 Simplify (add 8100 and 8100) 127.28 = c Take the square root of both sides of the equation

20. Correct!! Next

21. Incorrect Next a 2 + b 2 = c 2 10 2 + b 2 = 14 2 Plug numbers into formula 100 + b 2 = 196 Simplify squared values b 2 = 96 Simplify (subtract 100 from both sides) b = 9.8 ft Take the square root of both sides