Pythagorean Theorem Applications

Pythagorean Theorem Applications

The owners of a house want to convert a stairway leading from the ground to their back
porch into a ramp. The porch is 3 feet off the ground, and due to building regulations, the ramp
must start 12 feet away from the base of the porch. How long will the ramp be?

​​Example 1

Xavier walked 8 blocks due East and then 7 blocks due South. What is the shortest distance, in blocks, from the point where Xavier started to where he ended?

Example 2

You’re locked out of your house and the only open window is on the second floor, 30 feet above the ground. You need to borrow a ladder from one of your neighbors. There’s a flower garden along the edge of the house, so you’ll have to place the ladder 12 feet from the house. What length of ladder do you need to reach the window?

​​Example 3

Mary is trying to keep frogs from her garden. If her rectangle garden has a length of 15 inches and a width of 9 inches. What is the diagonal in inches of the garden?

Example 4

What is the height of the isosceles triangle with side lengths of 9 and a base of 14?

​​Example 5

Dylan wants to get from point A to point C as quickly as possible. He can climb the stairs directly from A to C at a rate of 10 meters per minute, or he can bike along the bike path from A to B to C at the rate of 30 meters per minute. If AB is perpendicular to BC, AB = 90 meters, and BC = 120 meters, which route will get Dylan to point C in less time?

​​Example 6

Math Response

Randy walked 7 blocks due East and then 6 blocks due South. What is the shortest distance, in blocks, from the point where Randy started to where he ended? Round your answer to the nearest tenth place.

Type answer here

Correct Answer: 9.2

Deg^°

Rad

Math Response

A water park wants to add a zipline into a pool. If the platform at the top of the zipline is 25
feet tall, and the pool is 40 feet long, what is the maximum length needed for the zipline? Round your answer to the nearest tenth.

Type answer here

Correct Answer: 47.2

Deg^°

Rad

Math Response

What is the height of the isosceles triangle with side lengths of 12 and a base of 20?

Type answer here

Correct Answer: 6.6

Deg^°

Rad

Math Response

Given a square with an area of 49 square units, determine the length of the diagonal.

Type answer here

Correct Answer: 9.9

Deg^°

Rad

Math Response

Stanley is traveling from point A to point B by taking a shortcut through the pond. A path
that avoids the pond is 25 feet south and 28 feet east. To the nearest tenth of a foot, how many feet will Stanley save by going through the pond instead of following the path?

Type answer here

Correct Answer: 15.5

Deg^°

Rad

Open Ended

Mary wants to get a computer monitor for her desk which can hold a monitor that is 16 inches wide and 10 inches high. Will a 22 inch monitor fit? Hint: tv monitors are measured by the diagonal.