Chapter 14 Answers - BISD Moodle

Chapter , Lesson 34.47. The tangent of an acute angle of a righttriangle is the ratio of the length of theopposite leg to the length of the adjacentleg.•48. = ≈ 2.2. (Because tan ∠X =and tan ∠XYZ = ,35. Equilateral triangles. The sides of each cellare equal to its radius; so the perimeter ofeach cell is 6r.36. Equilateral.•37. . [r is the hypotenuse of each 30°-60°right triangle included by ∆ABC; so thelength of the shorter leg is and the lengthof the longer leg is .AB = 2( ) = .]38. .•39. p = 2Nr = 2(3 sin 60°)r ≈ 5.196r.40. Yes. ≈ 5.196r.Ten Pentagons.•41. = 2.42. 36°. (∠X = = 36°.)43. 18°. (∠XYZ = = 18°.)•44. By the Law of Sines.•45. = ≈ 1.9.(Because = ,WZ = a tan ∠X = A tan ∠XYZ;so = .)Euclid’s Discovery.•49. 18°. ( = 18°.)50. 30°. ( = 30°.)51. 36°. ( = 36°.)•52. AX = 3.0901699 . . . . (sin 18° = ;so AX = 10 sin 18°.)53. BY = 5. (sin 30° = ; so BY = 10 sin 30°.)54. CZ = 5.8778525 . . . . (sin 36° = ;so CZ = 10 sin 36°.)55. a 2 = (2 AX) 2 = 38.19660 . . . .56. b 2 = (2 BY) 2 = 100.57. c 2 = (2 CZ) 2 = 138.19660 . . . .58. Euclid discovered that a 2 + b 2 = c 2 . If aregular decagon, hexagon, and pentagonare inscribed in circles of a given radius(or the same circle), the sum of the squaresof a side of the decagon and a side of thehexagon is equal to the square of a side ofthe pentagon.= = .)46. X and Y are equidistant from V and Z.(Two points each equidistant from theendpoints of a line segment determine theperpendicular bisector of the line segment.)