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Pythagorean Theorem Group Work Names _______________________________

For each Pythagorean theorem application problem, you are to first sketch out each problem, then show the steps that you have taken to solve. Make sure that you use the correct increments. (5 pts. Each) SHOW YOUR WORK, or no credit. 1. A telephone pole support cable attaches to the pole 20-feet high. If the cable is 25 feet long, how far from the bottom of the pole does the cable attach to the ground?

2. A mover’s ramp is placed on top of a 5-foot-high staircase. If the end of the ramp is on the floor 12-feet away, how long is the ramp?


3. The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder?

4. Donna's TV screen is 20 inches long. If the diagonal measures 25 inches, how long is the width of Donna's TV?

5. Town A is 9 miles from town B, and 12 miles from town C. A road connects towns B and C directly. Find the length of this road.

6. Scott wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point?


7. John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

8. A 13 feet ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder the top of The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall?

9. A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

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


11. What is the length of the diagonal of a 10 cm by 15 cm rectangle?

12. The diagonal of a rectangle is 25 in. The width is 15 inches. What is the length?

13. Two sides of a right triangle are 8 and 12. a. Find the missing side if 8 and 12 are legs.

b. Find the missing side if 8 and 12 are a leg and hypotenuse.

14. The area of a square is 81 square centimeters. Find the length of a side. Find the length of the diagonal.


15. An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. Find the height of the triangle.

16. A baseball diamond is a square that is 90 feet on each side. What is the distance from home to second base?

17. Shane marched 3 m east and 6 m north. How far is he from his starting point?

18. A power company employee is going to run a power line from the power pole to the back of Joel's house. Use the drawing below, and determine the approximate length of cable the employee will need.


19. The length of a rectangle is 24 cm and the width is 10 cm. How long is the diagonal?

20. Jackson is 54 miles from Lazy R Resort. Ontario is 31 miles south of Jackson. A land developer proposes building a shortcut road to directly connect Ontario and Lazy R. Draw a picture and find the length of this new road.

Pythagorean theorem  

applications to pythagorean theorem

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