2.5 Using The Pythagorean Theorem

Application of the Pythagorean Theorem:

Most of the time when learning mathematics, we spend our time learning the rules of how to the mathematics and little time is spent on where the mathematics is used. Part of the reason for is because the applications of mathematics in the real-world can be very complicated and relies on the understanding of mathematics learned in school. The Pythagorean Theorem is one of the more useful and simple mathematical ideas that is used in the real world. So let us take a look at some of the possibilities...

And by the way, ALWAYS DRAW OUT THE SITUATION!

Or as I like to say, "When in doubt, draw it out!"

Example A

Question: For the 130th anniversary of the Eiffel Tower, visitors will be able to ride a zip-line from the 2nd floor ( 117 meters above the ground ) to a point on the ground 800 meters away. How long is the cable used for the zip-line?	Watch the video: Zip-Line video:
Answer:

Example B

Question:

A farmer has a rectangular pasture with a gate on one of the corners and he wants to split the pasture into two equal size pastures. The farmer decides to put up a fence to run diagonally through the pasture so he can access the either pasture from the gate. If the pasture is a half mile long ( 880 yards ) and a quarter mile wide ( 440 yards ) how much wire will the farmer need to make a 4-wire high fence in the pasture?

Watch the video:

Answer:

Example C

Problem: You want to plant an Apple tree in your back yard. When you buy the tree, the nursery suggested that you stake the tree with 3-stakes placed around the tree in a circle. Each stake should be about 4 feet from the tree and the tree should be supported about 5 feet above the ground. How much rope will you need if you want to have an extra 2-feet at each end to tie the rope with?	Watch the video:
Answer:

Example D

Question: You decide to build a lean-to on the side of a shed. The side walls of the shed are 11ft tall to the eaves and you want the inside height of the shed to be 8ft. You have 12' sheet steel panels to use for the roof and you would like to have an over hang of at least a foot on the outside of the lean-to. How wide could you make the lean-to, if you round to the nearest foot?	Watch the video:
Answer:

Practice Problems

A. You are setting up a portable volleyball net. The top of the net is at the same height as the top of the poles which are 88.25 inches above the ground. An anchor rope is attached to the top of each pole. If the anchor rope is 12 feet long and is staked out in line with the net, about how far from the base of the pole will the stakes need to be placed?
B. In order to safely cross a river, a safety line needs to be strung between two trees on opposite sides of the river bank. When standing by a tree on the river bank and looking strait across the river, the tree on the opposite side is on a diagonal across the river If you walk to your left 10 yards you will be able to look straight across the river to the tree on the opposite side. From previous experience you know that the river is 27 feet wide. If you need at least 2-yards of rope to go around each tree, what is the shortest length of rope you need?
C. You just got a new drone! The maximum distance away from the transmitter that the drone can be before it automatically returns is 1,760 yards. The maximum allowable altitude that you can fly a drone at is 400 feet above the ground. How far away, horizontal distance, can the drone be before it will loose the signal from the transmitter.

Assignment:

Remember to draw out each situation and show all work/calculations done.

1. A screen door is sagging on one side and is out of square. A turnbuckle needs to be placed on the door ( as seen on the right ). If the door is 36 in 80 in ( W x H ) and one end of the turnbuckle is to be placed on the bottom right hand corner and the other end placed in the middle on the left side of the door. How long does the turnbuckle need to be?

2. The four corners of a pasture need to be constructed as pictured on the right. In each corner three 8-ft posts will be needed and 2-posts will need to be placed diagonally. The three 8-ft posts will each be placed in a 3-ft deep post hole that are dug 6-ft apart. The diagonal posts need to be attached at the *top* of the corner post and at the bottom of the other two posts ( see picture ). If the posts are sold in lengths of 6-ft, 8-ft, 10-ft, & 12-ft, what length posts are needed for the diagonal post?
3. The easternmost tower in the Euclid tower farm is located at 25659 130th Ave SW, is 750 feet tall, and belongs to Prairie Public Broadcasting. Red River Broadcasting's KBRR (10 Thief River Falls, Fox // KVRR), KGFE (2/15 Grand Forks), and KCGEDT (16 Crookston). There are six anchors, at ground level, for this tower, the inner three anchors are on a circumcenter of an equilateral triangle with a radius of 275-ft and the outer three anchor blocks are on a circumcenter of an equilateral triangle with a radius of 550-ft. Each anchor block has 3-cables attached to the tower. The inner anchor blocks have the lowest three anchor cables and the outer anchor blocks have the upper three anchor cables. The lowest anchor cable is attached to the tower 200-ft above the base of the tower. Each additional anchor cable is attached to the tower 100-ft above the cable below it. The last anchor cable is attached 700-ft above the base of the tower. Given this information, how many feet of anchor cable is used to stabilize this transmission tower?
4. A cable is used to help hold a gate, 16-ft long and 4-ft high, straight and square to its post. On the opposite side of this post, to where the gate is attached, is another post and these posts are 8-ft apart from each other and are each 6-ft tall ( sticking out of the ground ). The cable is attached to the top of the far end of the gate ( from the post attached to the gate ) then to the top of the post ( with the gate on it ) and to the base of the post on the opposite side of the gate. How long of a cable is needed if an extra 2-ft is needed at each end of the cable?
5. A fabric piping ( trim ) is to be used on the edges of a quilt and along the diagonals. If the finished size of the quilt is to be 90" x 108" ( " means inches ). How much will it cost for the piping, if the piping costs $0.99 per yard?