Pythagorean Theorem - Real Life Problems

Name _______________________________ Class _____ Date ___________

The Pythagorean Theorem – Real Life Problems

All the problems below can be solved using the Pythagorean Theorem. (Hint: It is

helpful to draw a diagram of the situation to help determine which measurements

refer to the legs and hypotenuse of the triangle.) Round all numbers to the nearest

tenth.

1. 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?

2. A baseball diamond is a square with sides of 90 feet. What is the shortest

distance between first base and third base?

3. Best Buy is selling 55 inch HD TV’s. This measurement is the diagonal

distance across the screen. If the screen measures 48 inches in width, what is

the actual height of the screen?

4. 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?

5. 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 his dog

house, in feet, at its tallest point?

6. You're locked out of your house and the only open window is

on the second floor, 25 feet above the ground. You need to

borrow a ladder from one of your neighbors. There's a bush

along the edge of the house, so you'll have to place the base

of the ladder 10 feet from the house. What length of ladder

do you need to reach the window?

7. Mrs. Stevens is building a slide for her kids. The ladder is 10 feet tall and the

slide is 15 feet long. What is the distance between the base of the ladder and

the bottom of the slide?

8. Andrew 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 travel from his starting point?

9. Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is

96 inches in diameter. Will the table fit through the front door? Explain.

10. The WBZ TV tower in Needham is almost 1300 ft. tall. One of the guy wires is

1385.6 feet long. It is attached to the tower 1200 ft. above the ground and is

anchored to the ground. How far from the base of the tv tower is the guy wire

attached to the ground?

11. Maggie has let out 50 meters of kite string when she notices that her kite is

flying directly above her friend Emily. If Emily is 35 meters from Maggie, how

high is the kite above the ground?

12. Mr. Kelly wants to make a small rectangular table. The sides of the piece of

wood he wants to use for the table top are 36" and 18". If the diagonal of the

piece of wood measures 43", is this piece of wood square? ("square" in this

case means the piece of wood has right angles at the corners.)