Pythagoras Word Problems

A ladder is leaning against a house at an angle of 39 degrees. If the ladder is 12 ft. long, how far is the bottom of the ladder from the house?

• 15.4 ft.

• 9.3 ft.

• 20.2 ft.

• 5.3 ft.

A new pipeline is being created to shorten the distance it has to travel to get from point A to point B. The original pipeline ran at a 90 angle from point A to point B and was 20 miles on one side and 15 miles on the other. The new pipeline will go straight from A to B. How much shorter will the new pipeline be?

• 10

• 25

• 175

• 625

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be? Which equation could be used to solve the problem?

A 25 foot ladder is leaning against a wall. The ladder is placed 10 feet away from the house. How far up the wall does the ladder reach?

Which diagram best represents the problem?

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The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide? Which equation could be used to solve the problem?

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run? Which equation could be used to solve the problem?

The bottom of a 13-foot ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? Which equation could be used to solve the problem?

How far from the base of a house do you need to place a 15 foot ladder so that is exactly reaches the top of a 12 foot wall? Which equation could be used to solve the problem?

• 12 + b = 15

The diagonal of a rectangle is 25 inches. The width is 15 inches. Which equation could be used to solve the problem?

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point? Which equation could be used to solve the problem?