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Warmup for Pythagorean Project

On your graph paper, do the following: Draw a triangle with the following sides: Leg 1 = 3 units (squares) Leg 2 = 4 units (squares) Draw the squares that the sides form. Find the area of each square. Warmup for Pythagorean Project. What is the relationship between the areas?

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Warmup for Pythagorean Project

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  1. On your graph paper, do the following: • Draw a triangle with the following sides: • Leg 1 = 3 units (squares) • Leg 2 = 4 units (squares) • Draw the squares that the sides form. • Find the area of each square. Warmup for Pythagorean Project What is the relationship between the areas? Try to write an equation for the relationship

  2. The relationship we just found is • Now let’s find the hypotenuse: • Please substitute what you know into the equation and follow PEMDAS to find . • How do we get rid of the exponent of 2? • Let’s make a flow map of this procedure. Now lets find the side length of the hypotenuse Square Them Add Them Square Root

  3. Project: • You will be given a situation and you are to solve it with the Pythagorean Theorem. You will create a poster with the following on it: • The situation in words • A picture of the situation with correct labels and units • The math that explains how to get the answer. • Your answer in a complete sentence (remember mmm… sentences from Math Modeling) • Round your answer to the nearest tenths place (_._) Using the Pythagorean theorem

  4. Pythagorean theorem project rubric

  5. Each side of a checkerboard measures 40 cm. What is the length of its diagonal? Checkerboard

  6. An inclined ramp rises 4 meters over a horizontal distance of 9 meters. How long is the ramp? Inclined ramp

  7. A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 4 meters from the base of the pole, how long is the wire? Guy wire

  8. A box is 120 cm. long and 25 cm. wide. What is the length of the longest ski pole that could be packed to lie flat in the box? Ski pole

  9. A television screen measures 30 cm. wide and 22 cm. high. What is the diagonal measure of the screen? television

  10. A ship leaves port and sails 12 kilometers west and then 19 kilometers north. How far is the ship from port? Ship leaving port

  11. The window of a burning building is 24 meters above the ground. The base of a ladder is placed 10 meters from the building. How long must the ladder be to reach the window? Burning building

  12. As Greg swam across an 80-meter river, the current carried him 30 m downstream. How far did he swim? swimming

  13. Two jets left Gerald R. Ford International Airport at the same time. One traveled east at 300 mph. The other traveled south at 400 mph. How far apart were the jets at the end of an hour? airplanes

  14. a receiver, who is 14 yards to the right of the quarterback, catches the ball 25 yards away from the line of scrimmage. How far did the quarterback throw the ball? football

  15. A helicopter rose vertically 300 m and then flew west 400 m. How far was the helicopter from its starting point? Helicopter

  16. A park is in the shape of a rectangle 8 miles long and 6 miles wide. How short is it to walk diagonally across the park? City park

  17. A newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3 ft. above the ground and then anchored to the ground 4 ft. from the base of the tree. How long is each wire? Planting a tree

  18. Two trains left Grand Rapids at the same time. One traveled south at 50mph. The other traveled east at 40mph. How far apart were the trains at the end of 1 hour? Trains

  19. A cable is stretched from the top of a cell phone tower to an anchor point on the ground 15 ft. from the base of the tower. The tower is 50 ft. tall. How long is the cable? Cell phone tower

  20. A tent is supported by a vertical stick in the middle of the tent that is 6 ft. tall. There is a rope attached to the top of the stick that is tied to a tent stake 8 ft. away from the middle stick. How long is the rope? Tent

  21. A builder needs to add diagonal braces to a wall. The wall is 16 ft. wide by 12 ft. high. How long does the builder have to cut each diagonal brace? Construction site

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