Unit 6: Pythagorean Theorem. 1. If two legs of a right triangle are 9 and 11, the hypotenuse is
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1 Name: ate: 1. If two legs of a right triangle are 9 and 11, the hypotenuse is 7. Triangle A is a right triangle with legs that measure 7 and 8. The length of the hypotenuse is If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse? 8. If the length of one leg of a right triangle is 5 and the length of the hypotenuse is 6, then the length of the other leg is The length of the hypotenuse of a right triangle is 13 centimeters and the length of one of the legs is 12 centimeters. Find the number of centimeters in the length of the second leg. 9. If the legs of a right triangle are 4 and 7, the length of the hypotenuse is If the length of one of the legs of a right triangle is 10 and the length of the other leg is 24, what is the length of the hypotenuse? 10. In the accompanying diagram, A is an equilateral triangle with a perimeter of In a right triangle, if the length of the hypotenuse is 15 and the length of one leg is 12, find the length of the other leg. What is the length of altitude h of this triangle? What is the length of the hypotenuse of a right triangle with legs of lengths 7 and 8? 11. The length of the hypotenuse of a right triangle is 15 and the length of one leg is 3. What is the length of the other leg? page 1
2 12. A wall is supported by a brace 10 feet long, as shown in the diagram. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach? 14. A woman has a ladder that is 13 feet long. If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house? The accompanying diagram shows a section of the city of Tacoma. High Road, State Street, and Main Street are parallel and 5 miles apart. Ridge Road is perpendicular to the three parallel streets. The distance between the intersection of Ridge Road and State Street and where the railroad tracks cross State Street is 12 miles. What is the distance between the intersection of Ridge Road and Main Street and where the railroad tracks cross Main Street? 15. If the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse? The NuFone ommunications ompany must run a telephone line between two poles at opposite ends of a lake, as shown in the accompanying diagram. The length and width of the lake are 75 feet and 30 feet, respectively. What is the distance between the two poles, to the nearest foot? page 2
3 17. The accompanying diagram shows a kite that has been secured to a stake in the ground with a 20-foot string. The kite is located 12 feet from the ground, directly over point X. What is the distance, in feet, between the stake and point X? 19. Theo determined that the correct length of the hypotenuse of the right triangle in the accompanying diagram is 20. Fiona found the length of the hypotenuse to be 2 5. Is Fiona s answer also correct? Justify your answer. 18. A builder is building a rectangular deck with dimensions of 16 feet by 30 feet. To ensure that the sides form 90 angles, what should each diagonal measure? 20. What is the value of x, in inches, in the right triangle below? 16 ft. 30 ft. 34 ft. 46 ft page 3
4 21. Nancy s rectangular garden is represented in the diagram below. 22. The end of a dog s leash is attached to the top of a 5-foot-tall fence post, as shown in the diagram below. The dog is 7 feet away from the base of the fence post. If a diagonal walkway crosses her garden, what is its length, in feet? How long is the leash, to the nearest tenth of a foot? page 4
5 Acces format version c EducAide Software Licensed for use by Problem-Attic Unit 6: Pythagorean Theorem 01/22/ miles Yes A
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