Pythagorean Theorem

a

b

ca2 + b2 = c2

Examples

12

5

c a2 + b2 = c2

122 + 52 = c2

144 + 25 = c2

169 = c2

c = 13

Examples cont.

a

9 m

17 m

a2 + b2 = c2

a2 + 92 = 172

a2 + 81 = 289

-81 -81

a2 = 208

a = 14.4

a = 14.4 m

Independent Practice

b

6 in.

11 in.

a2 + b2 = c2

62 + b2 = 112

36 + b2 = 121

-36 -36

b2 = 85

b = 9.2

b = 9.2 in.

Independent Practice cont.

3 ft.

2 ft.

c

a2 + b2 = c2

32 + 22 = c2

9 + 4 = c2

13 = c2

c = 3.6

c = 3.6 ft.

Word Problem/Real Life Example

• A cat is stuck at the top of a 38 ft. tree. A firefighter has a 50 ft. ladder. How far away from the base of the tree should the firefighter place the ladder?

50 ft.

b

38 ft.

382 + b2 = 502

1444 + b2 = 2500

-1444 -1444

b2 = 1056

b = 32.5

The ladder should be 32.5 ft. away from the base of the tree.