1. Objective The student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School

2. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. leg Hypotenuse right angle

3. The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a 2 + b 2 = c 2. Note: The hypotenuse, c, is always the longest side. c a b

4. Find the length of the hypotenuse if a = 12 and b = 16. 12 2 + 16 2 = c 2 144 + 256 = c 2 400 = c 2 Take the square root of both sides. 20 = c c 16 12

5. 5 2 + 7 2 = c 2 25 + 49 = c 2 74 = c 2 Take the square root of both sides. 8.60 = c 2. Find the length of the hypotenuse if a = 5 and b = 7. c 5 7

6. [Find the length of the hypotenuse given a=6 and b=12] A.[180] B.[324] C.[13.42] D.[18] c 12 6 12 2 +6 2 =C 2 144 +36 =C 2 180 =C 2

7. Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10. 4 2 + b 2 = 10 2 16 + b 2 = 100 Solve for b. 16 - 16 + b 2 = 100 - 16 b 2 = 84 b = 9.17

8. 4. Find the length of the leg, to the nearest hundredth, if c = 10 and b = 7. a 2 + 7 2 = 10 2 a 2 + 49 = 100 Solve for a. a 2 = 100 - 49 a 2 = 51 a = 7.14 10 a 7

9. Find the length of the missing side given a = 4 and c = 5 A.1 B.3 C.6.9 D.9 [Default] [MC Any] [MC All] 5 4 b 4 2 + b 2 = 5 2 16 + b 2 = 25 Solve for b. b 2 = 25 - 16 b 2 = 9 b= 3

10. 5. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle., 3, and 8 Which side is the biggest? The square root of 73 (= 8.5)! This must be the hypotenuse (c). Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

11. 9 + 64 = 73 73 = 73 Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle. Sides:, 3, and 8 3 2 + 8 2 = ( ) 2

12. Determine whether the triangle is a right triangle given the sides 6, 9, and 1.Yes 2.No 3.Purple

13. Determine if 6,9, and make a right triangle A.Yes B.No

14. A 10 ft ladder leans against an 8 foot tree. Find how far the bottom of the ladder is from the bottom of the tree. 6.0 0.1

15. Jane walks 5 miles East and 12 miles North. How far is she from her starting point? 13.0 0.1

16. Pythagorean Formula http://www.khanacademy.org/math/algebra/ ck12-algebra-1/v/distance-formula

17. Square the subtraction of the x’s Square the subtraction of the y’s Add the squares together Then take the square root Distance Y 2 – y 1 x 2 -x 1

18. Find the distance between A(4,8) and B(1,12) A (4, 8)B (1, 12) 3 4 3 2 +4 2 =c 2 25=c 2 5=c

19. [Find the distance between (-1,4) and (-7,-4) 8.0 0.1