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14. What is the side of a square whose diagonal is 50.0 m? 15. A rectangular park 125 m long and 233 m wide has a straight walk running through it from opposite corners. What is the length of the walk? 16. A ladder 32.0 ft long stands flat against the side of a building. How many feet. must it be drawn out at the bottom so that the top may be lowered 4.00 ft? 17. The slant height of a cone (Fig. 6-42) is 21.8 in., and the diameter of the base

14. What is the side of a square whose diagonal is 50.0 m? 15. A rectangular park 125 m long and 233 m wide has a straight walk running through it from opposite corners. What is the length of the walk? 16. A ladder 32.0 ft long stands flat against the side of a building. How many feet. must it be drawn out at the bottom so that the top may be lowered 4.00 ft? 17. The slant height of a cone (Fig. 6-42) is 21.8 in., and the diameter of the base

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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X 186 35.0 mm 36" FIGURE 6-46 '11 In 10 MATH 119 Textbook.... 45" 38.8 in FIGURE 6-47 FIGURE 6-43 7 16.0 in 12 6 T 0.500 FIGURE 6-48 16. FIGURE 6-49 30° FIGURE 6-50 15.8 in diameter 17 mm Section 3 Quadrilaterals High 2877 2025 f Chapter 6 Geometry FIGURE 6-44 Note: Angle B is not a right angle. B 100,4 Applications To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. 9. What is the cost, to the nearest dollar, of a triangular piece of land whose base is 828 ft and altitude is 412 ft at $1125 an acre? (1 acre = 43,560 ft²) 10. A vertical pole 45.0 ft high stands on level ground and is supported by three guy wires attached to the top and reaching the ground at distances of 60.0 ft, 108.0 ft, and 200.0 ft from the foot of the pole. What are the lengths of the wires? 0 11. A ladder 39.0 ft long reaches to the top of a building when its foot stands 15.0 ft from the building. How high is the building? FIGURE 6-45 12. Two streets, one 16.2 m and the other 31.5 m wide, cross at right angles. What is the diagonal distance between the opposite corners? 13. A rectangular room is 20.0 ft long, 16.0 ft wide, and 12.0 ft high. What is the diagonal distance from one of the lower corners to the opposite upper corner? 14. What is the side of a square whose diagonal is 50.0 m? 15. A rectangular park 125 m long and 233 m wide has a straight walk running through it from opposite corners. What is the length of the walk? 16. A ladder 32.0 ft long stands flat against the side of a building. How many feet must it be drawn out at the bottom so that the top may be lowered 4.00 ft? 17. The slant height of a cone (Fig. 6-42) is 21.8 in., and the diameter of the base is 18.4 in. How high is the cone? 18. Find the distance AB between the centers of the two rollers in Fig. 6-43. 19. A highway (Fig. 6-44) cuts a comer from a parcel of land. Find the number of acres in the triangular lot ABC. (1 acre = 43,560 ft) 20. A surveyor starts at A in Fig. 6-45 and lays out lines AB, BC, and CA. Find the three interior angles of the triangle. 21. Find dimension x on the beveled end of the shaft in Fig. 6-46. 22. A hex head bolt, Fig. 6-47, measures 0.500 in. across the flats. Find the distance x across the corners. Hint. You can solve problems involving a regular polygon by subdividing it into triangles. 23. An octagonal wall clock, Fig. 6-48, is to be 16.0 in. wide. Find the dimen- sion x. 31 24. Diagonal Brace: Find the length AB of the diagonal brace in Fig. 6-49. 25. Diagonal Brace: A brace A is to join rafter B (width = 3.25 in.) at an angle of 45", Fig. 6-50. Find the distance PQ by which A must be shortened to allow for the thickness of B. 26. Cross-Bridging: Find the length AB of the cross-bridging member in Fig. 6-51. 29. Project: Framing Square: Obtain a framing square and figure out how to use it to (a) lay out a miter cut (a cut of 45°) (b) draw an equilateral triangle (c) locate the center of a triangle (d) lay out an angle of 30° or 60. 27. A beam AB is supported by two crossed beams (Fig. 6-52). Find distance x. 28. Common Rafters: Figure 6-53 shows several kinds of roof rafters. A com mon rafter is one that runs from the ridge to the plate. It is common practice to figure rafter lengths from the building line to the centerline of the ridge board. This distance is called the line length, PQ in Fig. 6-54. This is later shortened by half the thickness of the ridge board and lengthened by the amount of overhang. Find the line length of a rafter that has a run of 14.0 ft and a slope of 8.0 in. per foot. 30. Project: A dissection proof is one in which a geometric figure is dissected or cut up, and the pieces rearranged to prove something. There are many dissection proofs of the Pythagorean theorem. Find a few of these, and choose one on which to make a classroom presentation. 31. Project: There are various kinds of "centers" of a triangle, including the cen- troid, the incenter, the circumcenter, and the orthocenter. Research and de- scribe how each is found. Can you find a use for any of them? -2.16 m VillerValley jack FIGURE 6-51 187 :
Transcribed Image Text:X 186 35.0 mm 36" FIGURE 6-46 '11 In 10 MATH 119 Textbook.... 45" 38.8 in FIGURE 6-47 FIGURE 6-43 7 16.0 in 12 6 T 0.500 FIGURE 6-48 16. FIGURE 6-49 30° FIGURE 6-50 15.8 in diameter 17 mm Section 3 Quadrilaterals High 2877 2025 f Chapter 6 Geometry FIGURE 6-44 Note: Angle B is not a right angle. B 100,4 Applications To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. 9. What is the cost, to the nearest dollar, of a triangular piece of land whose base is 828 ft and altitude is 412 ft at $1125 an acre? (1 acre = 43,560 ft²) 10. A vertical pole 45.0 ft high stands on level ground and is supported by three guy wires attached to the top and reaching the ground at distances of 60.0 ft, 108.0 ft, and 200.0 ft from the foot of the pole. What are the lengths of the wires? 0 11. A ladder 39.0 ft long reaches to the top of a building when its foot stands 15.0 ft from the building. How high is the building? FIGURE 6-45 12. Two streets, one 16.2 m and the other 31.5 m wide, cross at right angles. What is the diagonal distance between the opposite corners? 13. A rectangular room is 20.0 ft long, 16.0 ft wide, and 12.0 ft high. What is the diagonal distance from one of the lower corners to the opposite upper corner? 14. What is the side of a square whose diagonal is 50.0 m? 15. A rectangular park 125 m long and 233 m wide has a straight walk running through it from opposite corners. What is the length of the walk? 16. A ladder 32.0 ft long stands flat against the side of a building. How many feet must it be drawn out at the bottom so that the top may be lowered 4.00 ft? 17. The slant height of a cone (Fig. 6-42) is 21.8 in., and the diameter of the base is 18.4 in. How high is the cone? 18. Find the distance AB between the centers of the two rollers in Fig. 6-43. 19. A highway (Fig. 6-44) cuts a comer from a parcel of land. Find the number of acres in the triangular lot ABC. (1 acre = 43,560 ft) 20. A surveyor starts at A in Fig. 6-45 and lays out lines AB, BC, and CA. Find the three interior angles of the triangle. 21. Find dimension x on the beveled end of the shaft in Fig. 6-46. 22. A hex head bolt, Fig. 6-47, measures 0.500 in. across the flats. Find the distance x across the corners. Hint. You can solve problems involving a regular polygon by subdividing it into triangles. 23. An octagonal wall clock, Fig. 6-48, is to be 16.0 in. wide. Find the dimen- sion x. 31 24. Diagonal Brace: Find the length AB of the diagonal brace in Fig. 6-49. 25. Diagonal Brace: A brace A is to join rafter B (width = 3.25 in.) at an angle of 45", Fig. 6-50. Find the distance PQ by which A must be shortened to allow for the thickness of B. 26. Cross-Bridging: Find the length AB of the cross-bridging member in Fig. 6-51. 29. Project: Framing Square: Obtain a framing square and figure out how to use it to (a) lay out a miter cut (a cut of 45°) (b) draw an equilateral triangle (c) locate the center of a triangle (d) lay out an angle of 30° or 60. 27. A beam AB is supported by two crossed beams (Fig. 6-52). Find distance x. 28. Common Rafters: Figure 6-53 shows several kinds of roof rafters. A com mon rafter is one that runs from the ridge to the plate. It is common practice to figure rafter lengths from the building line to the centerline of the ridge board. This distance is called the line length, PQ in Fig. 6-54. This is later shortened by half the thickness of the ridge board and lengthened by the amount of overhang. Find the line length of a rafter that has a run of 14.0 ft and a slope of 8.0 in. per foot. 30. Project: A dissection proof is one in which a geometric figure is dissected or cut up, and the pieces rearranged to prove something. There are many dissection proofs of the Pythagorean theorem. Find a few of these, and choose one on which to make a classroom presentation. 31. Project: There are various kinds of "centers" of a triangle, including the cen- troid, the incenter, the circumcenter, and the orthocenter. Research and de- scribe how each is found. Can you find a use for any of them? -2.16 m VillerValley jack FIGURE 6-51 187 :
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