Chapter 14 Answers - BISD Moodle

((Chapter , ReviewArea Comparisons.23. πr 2 .•24. πr 2 . [ π(2r) 2 = πr 2 .]25. They are equal. Because α1 + α2 = α2 + α3,α1 = α3 by subtraction.26. The yellow and red areas are equal. (Thisfollows from the result of exercise 25 andthe symmetry of the figure.)Gothic Arch.27.the smaller circle shrinks to a point, the chordbecomes the diameter of the larger circle andthe expression for the area of the ring, πR – πr ,becomes πR , the area of the larger circle.In exercises through , the studentsdiscover a surprising property of the heart-shapedcurve: any line through point O divides its borderinto two equal parts. We would expect this resultof a line through the center of a figure that haspoint symmetry, but not of a figure that does not.Cup Problem.32. (Student answer.) (From the symmetry of thefigure, AG and BH evidently have equallengths, as do GD and HC. The two lowerarcs appear to be longer than the two upperones.)•33. 45°. (mAG = ∠ABG = 45°.)π•34. 0.79. [ 2π(1) = ≈ 0.79.]( (( (•35. – 1. (Because ABFE is a square, BE = .BG = BA = 1; so EG = BE – BG = – 1.)•28. ≈ 1.732. [ s 2 = (2) 2 .]•29. π ≈ 2.094. [ π(2) 2 = π.]30. π – ≈ 0.362.•31. π – ≈ 2.457. [ + 2( π – ) =+ π – = π – .]Set II (pages –)The answer to exercise , the width of theUnited States, is, of course, very approximate.The air distance between San Francisco andNew York City, both with latitudes close to °,is , miles; the coast of Maine is roughly miles east of New York City.Exercises through are based on thesurprising fact that, given two concentric circlesin which a chord of the larger circle is tangent tothe smaller circle, the area of the ring betweenthe circles is determined solely by the length ofthe chord, regardless of the sizes of the circles! As36. 135°. (mGD = ∠GED = 45° + 90° = 135°.)•37. 0.98. [ 2π( – 1) = π( – 1) ≈ 0.98.]38. (Student answer.)Time Zones.•39. About 1,037 mi. [π≈ 1,037.]•40. About 3,034 mi. [In ∆ABO,cos 40° (or sin 50°) = ;so AB = 3,960 cos 40° ≈ 3,034.]41. About 19,060 mi. [2π(3,034) ≈ 19,060.]•42. About 794 mi. ( ≈ 794.)43. Approximately 3,000 mi. (4 ⋅ 794 = 3,176.)