Pythagorean Theorem Word Problems



Name:_________________________________________________ Date: _________

Show your work on another sheet of paper. Sketch a picture of each situation and find the missing length. Round to the nearest hundredth. Put your answers in the blanks provided.

1. Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

2. Find the height of an equilateral triangle of 20 cm.

3. If the legs of an isosceles right triangle are 14 inches long, approximate the length of the hypotenuse to the nearest whole number.

4. Harley rides his bike 68 km south and then 6 km west. How far is he from his starting point?

5. If a leg of a triangle is 27 ft long, and another leg is 10 ft long, what is the length of the hypotenuse?

6. A baseball infield is in the shape of a square of sides 90 feet. What is the length from third base to first base?

7. If a side of a triangle is 28 ft long, and another side is 50 ft long, what is the length of the hypotenuse?

8. Town A is 90 miles form town B, and 18 miles form town C. Town A, B, and C are forming a right triangle at A. A road connects towns B and C directly. Find the length of this road.

9. Find the height of an equilateral triangle of 48 cm.

10. A cartoon measures 32 inches long and 16 inches high. What is the diagonal length of the box?

11. A rectangle is 7 cm wide and 10 cm long. Find the length of a diagonal of the rectangle.

12. A TV may be described in terms of the diagonal measure of its screen. If a TV screen is 16 inches by 12 inches, what is the length of its diagonal?

13. A 20 foot ladder is leaned against a wall. IF the base of the ladder is 8 feet from the wall, how high up on the wall will the ladder reach?

14. Jack has let out 40 meters of kite string when he observes that his kite is directly above Jill. If Jack is 25 meters from Jill, how far up in the sky is the kite?

15. A field hockey playing field is a rectangle 60 yards by 100 yards. What is the length of the diagonal from one corner of the field to the opposite corner?

16. You have just planted a new tree. To support the tree, you attach four guy wires from the trunk of the tree to stakes in the ground. Each guy wire has a length of 7 feet. Suppose you put the stakes in the ground 5 feet from the base of the trunk. Approximately how far up the trunk should you attach the guy wires?

17. Sonar of a Navy cruiser detects a submarine that is 2500 feet away. The point on the water directly above the submarine is 1500 feet away from the front of the cruiser. What is the depth of the submarine?

18. A rectangular swimming pool is 13 feet by 25 feet. What is the diagonal length from corner to corner?

19. A fish swims 10 yards north and 15 yards east from the boat that just caught it and threw it back. How many yards is the fish from the boat?

20. For “Surviorman” to get from point A to point B he must avoid walking through a swamp. To avoid the swamp, he must walk 34 meters south and 41 meters east. How many meters would be saved if it were possible to walk through the swamp?

21. Two joggers run 8 miles north and then 5 miles west. What is the shortest distance they must travel to return to their starting point?

22. “Survivorman” is swimming in a river. He is 4 feet from the bank and wants to get out. As he swims the river carries him downstream. He ends up 12 feet downstream from where you started. How far did you go?

23. A ramp for a wheelchair access is installed in a building. The height of the ramp is 1 foot. The length of the base of the ramp is 10 feet. How long is the ramp?

24. A flag pole is 15 feet tall. Its shadow is 20 feet long. If you stand at the edge of the shadow, how far are you from the top of the flag pole?

25. Your brother always walks on the sidewalk to get to school. He walks 6 blocks north and 2 blocks west. You cut through a field and walk straight to school. How much distance did you save?

26. A ladder is 25 feet long. The ladder needs to reach to a window that is 24 feet above the ground. How far away from the building should the bottom of the ladder be placed?

27. Suppose you leave your house and travel 13 miles west and then you travel 3 miles south. How far are you from your house?

28. Mrs. Smith just bought a big-screen TV set. The screen is 48 inches wide and 27 inches high. Find the length of its diagonal.

29. An 18 foot ladder is leaned against a wall. If the base of the ladder is 7 feet from the wall, how high up on the wall does the ladder reach?

30. Hulk left home and walked 8 blocks west. Then he turned and walked 6 blocks north. If each block is 500 feet long, how many feet is Hulk from home?

31. The lawn in front of Kermit Middle School is in the shape of a rectangle 30 yards long and 16 yards wide. How much shorter is your walk if you walk diagonally across the lawn rather than along two sides of it?

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