Pythagorean Theorem 2 a 2 b 2 c
Pythagorean Theorem 2 a + 2 b = 2 c
Parts of a Right Triangle Leg a Hypotenuse c (Longest Side) [Opposite the 90° angle] Leg b
Example 1 Is the triangle below a right triangle? a 2 + b 2 = c 2 5 4 42 + 3 2 = 5 2 16 + 9 = 25 25 = 25 3 YES
Example 2 Is the triangle below a right triangle? 14 5 a 2 + b 2 = c 2 52 + 122 = 142 25 + 144 = 196 169 = 196 NO 12 ?
YOUR TURN Is the triangle below a right triangle? 15 9 a 2 + b 2 = c 2 92 + 122 = 152 81 + 144 = 225 YES 12 ?
Example 3 Find the missing side length a 13 12 a 2 + b 2 = c 2 a 2 + 122 = 132 a 2 + 144 = 169 -144 =-144 2 = 25 a √ √ a=5
Find the missing side length a 2 + b 2 = c 2 a 30 ft 24 ft
Workbook Pg. 7 -- #2 Find the missing side length 24 in 10 in c a 2 + b 2 = c 2 102 + 242 = c 2 100 + 576 = c 2 2 676 = c √ √ 26 = c
Workbook Pg. 7 -- #3 Find the missing side length 17 cm b a 2 + b 2 = c 2 82 + b 2 = 172 8 cm 64 + b 2 = 289 -64 = -64 2 = 225 b √ √ b = 15
Workbook Pg. 7 -- #4 Find the missing side length x 8 m 5 m a 2 + b 2 = c 2 82 + 5 2 = x 2 64 + 25 = x 2 2 89 = x √ √ 9. 433981132 = x Round to the nearest 9. 4 = tenth x
Workbook Pg. 7 -- #5 Find the missing side length x 2 + b 2 = c 2 a 6. 2 cm x 2 + 6. 22 = 7. 52 x 2 + 38. 44 = 56. 25 -38. 44 7. 5 cm 2 = 17. 81 x √ √ x = 4. 220189569 Round to the nearest x = tenth 4. 2
Workbook Pg. 7 -- #6 Find the missing side length 2 + b 2 = c 2 a x 8 in x 2 + 82 = 152 x 2 + 64 = 225 -64 15 in √ x 2 =√ 161 x = 12. 68857754 x = 12. 7 Round to the nearest tenth
Workbook Pg. 7 -- #7 A ladder leans against a wall 6 ft above the ground. The base of the ladder is 3 ft from the wall. How long is the ladder? La d de r a 2 + b 2 = c 2 62 + 3 2 = x 2 x 36 + 9 = x 2 √ 45 =√ x 2 6. 708203932 = x Round tenth 6. 7 to = xthe nearest ground 3 ft W A 6 ft L L
Workbook Pg. 7 -- #8 A small rectangular tray measures 16 cm by 18 cm. How long is the diagonal? a 2 + b 2 = c 2 x TRAY 18 cm 182 + 162 = x 2 324 + 256 = x 2 2 16 cm 580 = √ x √ 24. 08318916 = x Round to the nearest tenth 24. 1 = x
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