PYTHAGOREAN THEOREM

PYTHAGOREAN TRIPLES (3, 4, 5) (6, 8, 10) (12, 16, 20) (5, 12, 13) (10, 24, 26) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (20, 21, 29)

# 1. In a right triangle, if “a” and “b” represent the lengths of the legs and “c” represents the length of the hypotenuse, find the missing side length in each of the following: c = 26 (a.) a = 10, b = 24 ______ a2 + b2 = c2 a = 9.38 (b.) a = 9, c = 13 ______ c2 – b2= a2

# 1. In a right triangle, if “a” and “b” represent the lengths of the legs and “c” represents the length of the hypotenuse, find the missing side length in each of the following: a = 24 (c.) b = 18, c = 30 ______ c2 – b2= a2 b = 8 (d.) a = 6, c = 10 ______ c2 – a2= b2

Find the value of x using the Pythagorean Theorem. # 2. 5 Find the value of x using the Pythagorean Theorem. 12 x2 = 52 + 122 x x = ______ 13

Find the value of x using the Pythagorean Theorem. # 3. x 8 x2 = 102 – 82 10 Find the value of x using the Pythagorean Theorem. x = ______ 6

Find the value of x using the Pythagorean Theorem. # 4. 5 x2 = 52 – 32 x Find the value of x using the Pythagorean Theorem. 3 4 x = ______

Find the value of x using the Pythagorean Theorem. # 5. Find the value of x using the Pythagorean Theorem. 13 5 x2 = 132 – 52 x 12 x = ______

Find the value of x using the Pythagorean Theorem. # 6. Find the value of x using the Pythagorean Theorem. x x2 = 162 + 632 63 16 65 x = ______

Find the value of x using the Pythagorean Theorem. # 7. 56 x 65 x2 = 652 – 562 Find the value of x using the Pythagorean Theorem. 33 x = ______

# 8. AB2 = 342 + 412 AB = 53.3 (34 + 41) – 53.3 75 – 53.3 = 21.7 To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? (A.) 22 (B.) 34 (C.) 53 (D.) 75

# 9. 90 ft. 90 ft. d2 = 902 + 902 d 90 ft. 90 ft. d = 127.3 ft. A baseball diamond is a square with sides of 90 feet. What is the shorter distance, to the nearest tenth of a foot, between first and third base? (A.) 90.0 (B.) 127.3 (C.) 180.0 (D.) 180.7

# 10. d2 = 182 + 242 18 in. d d = 30 ft. 24 in. A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase to the nearest tenth of a foot? (A.) 2.5 (B.) 2.9 (C.) 26.5 (D.) 30.0

# 11. x2 = 192 – 102 19 in. 10 in. x x = 16.16 In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch? (A.) 10 (B.) 14 (C.) 16 (D.) 19

# 12. d2 = 5.252 + 5.252 d 5.25 5.25 d = 7.42 The older floppy diskettes measured 5 ¼ inches on each side. What was the diagonal length of the diskette to the nearest tenth of an inch? (A.) 5.3 (B.) 6.5 (C.) 7.4 (D.) 7.6

# 13. Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5. She asks you to find the other leg of the triangle without using a paper and pencil. What is your answer? (A.) 5 (B.) 8 (C.) 10 (D.) 12

5 mi. # 14. d2 = 52 + 82 8 mi. d d = 9.4 Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? (A.) 8.4 (B.) 9.5 (C.) 9.4 (D.) 13.1

# 15. (A.) 6 (B.) 8 (C.) 10 (D.) 12

# 16. Oscar’s dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of the dog house, in feet, at its tallest point? 3 (A.) 3 (B.) 4 (C.) 4.5 (D.) 5

# 17. Seth made a small rectangular table for his workroom. The sides of the table are 36” and 18”. If the diagonal of the table measures 43”, is the table a square? A table which is “square” has right angles at the corners. 362 + 182 = 1296 + 324 = 1620 (A.) Yes (B.) No 432 = 1849

What is the length of the diagonal in yards? # 18. Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as shown in the diagram. What is the length of the diagonal in yards? (A.) 50 (B.) 60 (C.) 70 (D.) 80

# 19. In a right triangle, the shorter leg is 7 units less than the longer leg. The hypotenuse is 1 unit more than the longer leg. Find the length of the shorter leg. 12 x = longer leg 5 x – 7 = shorter leg 13 x + 1 = hypotenuse

# 20. In a right triangle, the shorter leg is 5 and the hypotenuse is one unit more than the longer leg. Find the length of the hypotenuse. 12 x = longer leg 5 = shorter leg x + 1 = hypotenuse 13

# 21. The hypotenuse of a right triangle is 1 more than twice the length of the shorter leg. The longer leg is 15. Find the hypotenuse. 15 = longer leg 8 x = shorter leg 2 x + 1 = hypotenuse 17

# 22. The foot of a ladder is 10 feet from a wall. The ladder is 2 feet longer than the height it reaches on the wall. What is the length of the ladder? 26 h + 2 h 24 10

# 23. Town A is 65 km due north of Town B. Town C is 44 km due east of town B. Find the distance from Town A to Town C. A AC2 =652 + 442 65 B 44 C AC = 79.5 km

# 24. How far from the base of a house do you need to place a 15-foot ladder so that it exactly reaches the top of a 12-foot wall? 15 12 x 9

# 25. John leaves school to go home. He walks 6 blocks North and then 8 blocks West. How far is John from the school? 8 6 10

Which could be the lengths of the sides of a right triangle? # 26. Which could be the lengths of the sides of a right triangle? YES (a.) 8, 15, 17 ______ NO (b.) 7, 25, 26 ______ YES (c.) 9, 12, 15 ______ YES (d.) 24, 45, 51 ______