Basic Mathematics for College Students

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APPLICATIONS

41. ADJUSTING LADDERS A 20-foot ladder reaches
    a window 16 feet above the ground. How far from the
    wall is the base of the ladder?


42. LENGTH OF GUY WIRES A 30-foot tower is to be
    fastened by three guy wires attached to the top of the
    tower and to the ground at positions 20 feet from its
    base. How much wire is needed? Round to the
    nearest tenth.


43. PICTURE FRAMES After gluing and nailing two
    pieces of picture frame molding together, a frame
    maker checks her work by making a diagonal
    measurement. If the sides of the frame form a right
    angle, what measurement should the frame maker
    read on the yardstick?


44. CARPENTRY The gable end of the roof shown is
    divided in half by a vertical brace, 8 feet in height.
    Find the length of the roof line.


45. BASEBALL A baseball diamond is a square with
    each side 90 feet long. How far is it from home
    plate to second base? Round to the nearest
    hundredth.

90 ft

90 ft

30 ft

8 ft

?

?

20 in.

15 in.

752 Chapter 9 An Introduction to Geometry

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GUIDED PRACTICE

Find the length of the hypotenuse of the right triangle shown

below if it has the given side lengths.See Examples 1 and 2.

13. ft and ft


14. mm and mm


15. m and m


16. in. and in.


17. mi and mi


18. ft and ft


19. cm and cm


20. mm and mm
    Refer to the right triangle below.See Example 3.


21. Find if cm and cm.


22. Find if in. and in.


23. Find if m and m.


24. Find if yd and yd.


25. Find if m and m.


26. Find if yd and yd.


27. Find if m and m.


28. Find if ft and ft.
    The lengths of two sides of a right triangle are given. Find the
    missing side length. Give the exact answer and an approximation
    to the nearest hundredth.See Example 4.


29. cm and cm


30. in. and in.


31. m and m


32. ft and ft


33. in. and in.


34. mi and mi


35. in. and in.


36. mm and mm

Is a triangle with the following side lengths a right triangle?

See Example 5.

37. 12, 14, 15


38. 15, 16, 22


39. 33, 56, 65


40. 20, 21, 29

b 9 c 12

b 4 c 6

a 5 b 7

a 9 b 3

a 10 b 4

a 12 b 8

a 4 c 8

a 5 c 6

b a 630 c 650

b a 180 c 181

a b 16 c 34

a b 21 c 29

a b 9 c 41

a b 18 c 82

b a 14 c 50

b a 10 c 26

a 132 b 85

a 88 b 105

a 80 b 39

a 48 b 55

a 16 b 12

a 5 b 12

a 12 b 9

a 6 b 8

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