Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Use the triangle below. Find the missing side length. If necessary, round to the nearest tenth.

6. a = 3 , b = 4 eh equals 3 comma b equals 4
7. a = 6 , c = 10 eh equals 6 comma c equals 10
8. b = 1 , c = 5 4 b equals 1 comma c equals , 5 fourths
9. a = 5 , c = 13 eh equals 5 comma c equals 13
10. a = 0.3 , b = 0.4 eh equals 0.3 comma b equals 0.4
11. a = 8 , b = 15 eh equals 8 comma b equals 15
12. a = 1 , c = 5 3 eh equals 1 comma c equals , 5 thirds
13. b = 6 , c = 7.5 b equals 6 comma c equals 7.5
14. b = 3.5 , c = 3.7 b equals 3.5 comma c equals 3.7
15. a = 1.1 , b = 6 eh equals 1.1 comma b equals 6
16. a = 8 , c = 17 eh equals 8 comma c equals 17
17. a = 9 , b = 40 eh equals 9 comma b equals 40
18. b = 2.4 , c = 7.4 b equals 2.4 comma c equals 7.4
19. a = 4 , b = 7.5 eh equals 4 comma b equals 7.5
20. a = 0.9 , c = 4.1 eh equals 0.9 comma c equals 4.1
21. Fitness A jogger goes half a mile north and then turns west. If the jogger finishes 1.3 mi from the starting point, how far west did the jogger go?
22. Construction A construction worker is cutting along the diagonal of a rectangular board 15 ft long and 8 ft wide. What will be the length of the cut?

See Problem 3.

Determine whether the given lengths can be side lengths of a right triangle.

23. 15 ft, 36 ft, 39 ft
24. 12 m, 60 m, 61 m
25. 13 in., 35 in., 38 in.
26. 16 cm, 63 cm, 65 cm
27. 14 in., 48 in., 50 in.
28. 16 yd, 30 yd, 34 yd

B Apply

29. Swimming A swimmer asks a question to a lifeguard sitting on a tall chair, as shown in the diagram. The swimmer needs to be close to the lifeguard to hear the answer. What is the distance between the swimmer's head and the lifeguard's head?

Any set of three positive integers that satisfies the equation a 2 +   b 2 =   c 2 bold italic eh squared , plus , bold italic b squared , equals , bold italic c squared  is a Pythagorean triple. Determine whether each set of numbers is a Pythagorean triple.

30. 11, 60, 61
31. 13, 84, 85
32. 40, 41, 58
33. 50, 120, 130
34. 32, 126, 130
35. 28, 45, 53
36. Think About a Plan A banner shaped like a right triangle has a hypotenuse of length 26 ft and a leg of length 10 ft. What is the area of the banner?
    • What information do you need to find the area of a triangle?
    • How can you find the length of the other leg?

37. History Originally, each face of the Great Pyramid of Giza was a triangle with the dimensions shown. How far was a corner of the base from the pyramid's top? Round to the nearest foot.

    

38. Two sides of a right triangle measure 10 in. and 8 in.
    1. Writing Explain why this is not enough information to be sure of the length of the third side.
    2. Give two possible values for the length of the third side.

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