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Pythagorean theorem PROBLEM SOLVING

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WARM UP A pool is shaped like a rectangle with a length 4 times the width. What is an expression for the distance between opposite corners of the pool? Simplify: 𝟓𝒏 −𝟒 = 6 What is the solution of 𝟔𝒈 −𝟐𝟑 = 𝟏𝟐 −𝒈 Simplify: ( 𝟓 )(7 - 𝟓 )

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**Today you are going to be working in groups to solve some Pythagorean word problems.**

While working on your problems, be sure to: have a diagram to depict the problem have the formula written out show all work Be ready to explain HOW you solved your problems.

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**To get from point A to point B you must avoid walking through a pond**

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 tenth of a meter, how many meters would be saved if it were possible to walk through the pond?

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**A baseball diamond is a square. The length of the square is 100 ft**

A baseball diamond is a square. The length of the square is 100 ft. How far would the catcher have to throw the ball from the home plate to the second base?

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You drive three miles west, then 5 miles south, and finally 15 miles east. How far will you end up from where you started?

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**Andy is standing in the middle of a large field throwing baseballs**

Andy is standing in the middle of a large field throwing baseballs. He throws the first ball 20 yards straight out. He turns 90 degrees to the right and throws a second ball 23 yards straight out. He turns 90 degrees to the right again and throws a third ball 45 yards (straight out again). What is the shortest distance he can walk to retrieve all three balls? He does not need to return to his original spot. Round your answer to the nearest 10th.

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**Tim is trying to protect his triangular garden**

Tim is trying to protect his triangular garden. The base is 6 feet long and the height is 8 feet tall. If the fence costs $15 per foot, how much will the fence cost?

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**Frank Road and James Road make a perpendicular intersection**

Frank Road and James Road make a perpendicular intersection. The state wants to build a new road. The new road will intersect 3 miles north of the intersection on Frank Road and 4 miles west of the intersection on James Road. How long will the new road be that intersects Frank and James Road? The new road would cost $10 per foot to pave. What would be the cost of the new road?

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The mobile phone company is anchoring wires to the top of their 1200 feet high communication towers. The cable for the support wire comes in a roll that is 3900 feet long. The company requires you to use the entire roll. The cable can only be cut twice to ensure strength. All cables need to be equal in length. How long will each cable be and how far from the base of the tower do they need to be anchored?

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**In the city planning meeting, a scale drawing of a park was drawn**

In the city planning meeting, a scale drawing of a park was drawn. The park fills inside a square city block. The scale was 3 inches equal to 3/10 miles. One side of the city block was 4 inches in the drawing. One member of the city planners said: “Their needs to be a short cut through the park from the corners.” How long in miles will the short cut be? Round your answers to the nearest tenth of a mile?

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**A 4. 5 m pipe rests on a 2 m high fence**

A 4.5 m pipe rests on a 2 m high fence. One end of the pipe is on the ground 3 m from the base of the fence. How much of the pipe overhangs the fence?

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You are planning to put a new digital flat TV on a wall that is 12 feet long and 9 feet high. The digital TV has a diagonal of 72 inches. The length of the TV is twice the width of the TV. How much of the wall will still need to be decorated around the TV?

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A 50 foot ladder rests against a wall so that the top of the ladder is 48 feet from the ground. As you start to climb the ladder, it slips and the top of the ladder drops 8 feet. How far does the bottom of the ladder slide away from the wall (from its original position)?

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**Two ships B and C leave a port A at the same time**

Two ships B and C leave a port A at the same time. B travels due west at a constant speed of 16 km/h. C travels due south at a constant speed of 18 km/h. How far have B and C each travelled in two hours? Find the distance between them after two hours.

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**A lifeguard spots a drowning swimmer 40 feet from the beach**

A lifeguard spots a drowning swimmer 40 feet from the beach. She runs 90 feet along the beach at a speed of 15 feet per second, then jumps in the water and swims straight to the swimmer at a speed of 5 feet per second. How long does it take her to reach the swimmer?

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**A square has an area of 225 m².**

Find the length of one side of the square. Determine the perimeter of the square. What is the length of the square’s diagonal.?

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**Jessica’s cat is stuck in a tree**

Jessica’s cat is stuck in a tree. The fire department no longer assists in getting cats out of trees. Jessica’s dad knows the cat is approximately 22 feet high. He has a 25 foot ladder and the directions say to be safe he must keep the base of the ladder 10 feet from the base of the tree. Will the ladder reach the cat so he can safely get it out of the tree?

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Juan drove from Portland to Ashland on Interstate 5, then from Ashland to Klamath Falls on Highway 66. Assume that I-5 goes directly south and Highway 66 goes directly east. It is 280 miles from Portland to Ashland and 64 miles from Ashland to Klamath Falls. How many total miles did Juan travel? If a road was built directly from Portland to Klamath Falls, how long would it be? Round your answer to the nearest mile. Approximately how much shorter would Juan’s trip be if he was able to take the direct route.

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(3, 4, 5)(6, 8, 10)(12, 16, 20) (5, 12, 13)(10, 24, 26) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (20, 21, 29) PYTHAGOREAN TRIPLES.

(3, 4, 5)(6, 8, 10)(12, 16, 20) (5, 12, 13)(10, 24, 26) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (20, 21, 29) PYTHAGOREAN TRIPLES.

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