7 The Pythagorean Theorem
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1 HPTER 7 The Pythagorean Theorem Lesson 7.1 Understanding the Pythagorean Theorem and Plane Figures For each figure, shade two right triangles and label the hypotenuse of each triangle with an arrow Find the value of x. 3. x cm 7 cm 4. x cm 24 cm 7.5 cm 10 cm cm 26 cm x cm 6. x cm 41 cm 40 cm Extra Practice ourse 3 1
2 alculate each unknown side length. Round your answer to the nearest tenth in. x in. y in. x in. D 8 in. 11 in. 8.8 in. 10 in. 12 in x in. 20 in. 16 in. 4 in. y in. 11 in. y in. x in. 7 in. 11. Fritz mows two triangular fields. Determine which field is a right triangle. 60 m 36 m 48 m Field Field 40 m 60 m 50 m 2 hapter 7 Lesson 7.1
3 12. lan placed a ladder against a wall. The bottom of the ladder was 5 feet away from the wall. Find the height of the wall. Ladder 10 ft Wall 5 ft 13. One end of a cable is attached to the top of a flagpole and the other end is attached 6 feet away from the base of the pole. If the height of the flagpole is 12 feet, find the length of the cable. able Flagpole 12 ft 14. n escalator runs from the first floor of a shopping mall to the second floor. The length of the escalator is 30 feet and the distance between the floors is 12 feet. Find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator. Escalator 30 ft 6 ft Second floor 12 ft First floor Extra Practice ourse 3 3
4 15. hot air balloon is attached to the ground by a taut 100-meter cable, as shown in the diagram. Find the vertical height of the balloon above the ground. Hot air balloon able 100 m 20 m 16. taut cable connects two cable car stations and which are positioned 50 meters and 20 meters above the ground. The horizontal distance between the stations is 1 kilometer. Find the length of the cable m Station able km m Station 17. whiteboard is 6 feet long and 3 feet wide. Find the length of the longest straight line that can be drawn on the whiteboard. 4 hapter 7 Lesson 7.1
5 18. Sono Road runs from South to North and Ewest Road runs from East to West intersecting at point X. Jeb and Jill are at point P on Sono Road 30 meters from point X. Jeb walks along Sono Road to point X then turns east and walks 20 meters to point Q on Ewest Road. Jill walks on a path linking point P to point Q. Find the difference in distance between the two routes. X Ewest Road 20 m Q Sono Road 30 m Path N W E P S foot vertical pole has two strings of equal length attached to it at different points. The other end of one string, represented by in the diagram is tethered to the ground 12 feet from the base of the pole. The other end of the other string, represented by D in the diagram is tethered to the ground 13 feet from the base of the pole. a) Find the length of the string. b) Find the distance between the points and. 12 ft 15 ft E 13 ft D Extra Practice ourse 3 5
6 20. The diagonal of a square piece of cardboard is 28 inches. a) Find the perimeter of the square. b) Find the area of the square. 21. In the diagram, m D is 90, D is 22.6 inches, is 13 inches, and is 34.4 inches. a) Find the length of. b) Find the area of triangle D in. 13 in. D 22.6 in. 6 hapter 7 Lesson 7.1
7 22. Points,, and are corners of a triangular field where m is 90, is 40 meters and is 45 meters. a) Find the length of. 40 m 45 m b) John walks along the edge of the field from point to point. If P is the point on when John is nearest to point, find the length of P. 23. In rectangle PQRT, PQ is 80 feet, QR is 65 feet, RS is 30 feet, and m SUP is 90. a) Find the perimeter of the shaded triangle. P 80 ft Q b) Find the area of the shaded triangle. c) Find the length of SU. T S U 30 ft R 65 ft Extra Practice ourse 3 7
8 24. map with a scale of 1 : 50,000 shows the locations of four towns,,, and D. The distance between Town and Town is 6 centimeters, the distance between Town and Town is 7 centimeters, and the distance between Town and Town D is 8 centimeters. Given that m 5 m D 5 90, find the actual distance between Town and Town D. 8 cm D 7 cm 6 cm 25. In the diagram, is 20 meters, is 65 meters, D is 60 meters, D is 16 meters, and D is 25 meters. Determine if triangle D and triangle D are right triangles. Explain. 16 m D 20 m 25 m 60 m 65 m 8 hapter 7 Lesson 7.1
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