#16 X18635.0 mm36"FIGURE 6-46'11In10MATH 119 Textbook....45"38.8 inFIGURE 6-47FIGURE 6-43716.0 in126T0.500FIGURE 6-4816.FIGURE 6-4930°FIGURE 6-5015.8 indiameter17 mmSection 3 QuadrilateralsHigh28772025 fChapter 6 GeometryFIGURE 6-44 Note: Angle B is not aright angle.B100,4ApplicationsTo help you solve each problem, draw a diagram and label it completely. Look forspecial triangles or right triangles contained in the diagram. Be sure to look up anyword that is unfamiliar.9. What is the cost, to the nearest dollar, of a triangular piece of land whose baseis 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 bythree guy wires attached to the top and reaching the ground at distances of60.0 ft, 108.0 ft, and 200.0 ft from the foot of the pole. What are the lengthsof the wires?011. A ladder 39.0 ft long reaches to the top of a building when its foot stands15.0 ft from the building. How high is the building?FIGURE 6-4512. Two streets, one 16.2 m and the other 31.5 m wide, cross at right angles. Whatis 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 isthe diagonal distance from one of the lower corners to the opposite uppercorner?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 runningthrough 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 feetmust 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 baseis 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 ofacres 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 thethree 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 distancex across the corners. Hint. You can solve problems involving a regular polygonby subdividing it into triangles.23. An octagonal wall clock, Fig. 6-48, is to be 16.0 in. wide. Find the dimen-sion x.3124. 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 of45", Fig. 6-50. Find the distance PQ by which A must be shortened to allow forthe thickness of B.26. Cross-Bridging: Find the length AB of the cross-bridging member inFig. 6-51.29. Project: Framing Square: Obtain a framing square and figure out how to useit 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 common rafter is one that runs from the ridge to the plate. It is common practiceto figure rafter lengths from the building line to the centerline of the ridgeboard. This distance is called the line length, PQ in Fig. 6-54. This is latershortened by half the thickness of the ridge board and lengthened by theamount 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 cutup, and the pieces rearranged to prove something. There are many dissectionproofs of the Pythagorean theorem. Find a few of these, and choose one onwhich 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 mVillerValley jackFIGURE 6-51187:

Question

#16 X18635.0 mm36&#34;FIGURE 6-46'11In10MATH 119 Textbook....45&#34;38.8 inFIGURE 6-47FIGURE 6-43716.0 in126T0.500FIGURE 6-4816.FIGURE 6-4930°FIGURE 6-5015.8 indiameter17 mmSection 3 QuadrilateralsHigh28772025 fChapter 6 GeometryFIGURE 6-44 Note: Angle B is not aright angle.B100,4ApplicationsTo help you solve each problem, draw a diagram and label it completely. Look forspecial triangles or right triangles contained in the diagram. Be sure to look up anyword that is unfamiliar.9. What is the cost, to the nearest dollar, of a triangular piece of land whose baseis 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 bythree guy wires attached to the top and reaching the ground at distances of60.0 ft, 108.0 ft, and 200.0 ft from the foot of the pole. What are the lengthsof the wires?011. A ladder 39.0 ft long reaches to the top of a building when its foot stands15.0 ft from the building. How high is the building?FIGURE 6-4512. Two streets, one 16.2 m and the other 31.5 m wide, cross at right angles. Whatis 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 isthe diagonal distance from one of the lower corners to the opposite uppercorner?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 runningthrough 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 feetmust 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 baseis 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 ofacres 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 thethree 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 distancex across the corners. Hint. You can solve problems involving a regular polygonby subdividing it into triangles.23. An octagonal wall clock, Fig. 6-48, is to be 16.0 in. wide. Find the dimen-sion x.3124. 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 of45&#34;, Fig. 6-50. Find the distance PQ by which A must be shortened to allow forthe thickness of B.26. Cross-Bridging: Find the length AB of the cross-bridging member inFig. 6-51.29. Project: Framing Square: Obtain a framing square and figure out how to useit 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 common rafter is one that runs from the ridge to the plate. It is common practiceto figure rafter lengths from the building line to the centerline of the ridgeboard. This distance is called the line length, PQ in Fig. 6-54. This is latershortened by half the thickness of the ridge board and lengthened by theamount 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 cutup, and the pieces rearranged to prove something. There are many dissectionproofs of the Pythagorean theorem. Find a few of these, and choose one onwhich to make a classroom presentation.31. Project: There are various kinds of &#34;centers&#34; 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 mVillerValley jackFIGURE 6-51187:

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