Arcs

AJ
by Anjie Julseth74 views·Updated Feb 7, 2021
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  1. Hi, guys.
  2. Miss Joel.
  3. Seth here.
  4. And it's time for another episode of wearing Colorado is
  5. your math teacher.
  6. And pardon?
  7. The wind is very windy where I'm at.
  8. Okay, join me as we study arcs.
  9. Arcs are everywhere.
  10. A rainbow is an ark.
  11. Copy this down in your notes and pas me so
  12. you can get it all down and draw the pictures
  13. to please.
  14. Okay, so we've already talked about our measure is the
  15. same as the degrees of the central angle.
  16. But we haven't talked about our length, which is, actually,
  17. if you measure the pizza crust, um and that's gonna
  18. be degrees divided by 3.
  19. 60 times two pi r, because arc length is a
  20. portion of the circumference.
  21. Okay, So arc measures in degrees, like I just said,
  22. and you write it little m with two capital letters.
  23. The beginning of the artery ended the arguments A minor
  24. less than 180 degrees or three capital letters.
  25. If it's a major arc greater than 180 degrees, but
  26. less than 3.
  27. 60. And you put that little arc over it.
  28. So park like this.
  29. The length of the ark measured in inches centimeters or
  30. feet, and it's a portion of the circumference.
  31. So the formula is gonna be degrees over 3 60.
  32. That gives you what portion of the circle it is.
  33. And then times two pi r, which is the circumference.
  34. Here's another arc.
  35. I have lots of pictures of arcs in here.
  36. All right, one more time.
  37. Here is the formula.
  38. So look, that's a minor arc from a point A
  39. to point B.
  40. And so to find the arc length, we do the
  41. measure in degrees of a B over 3.
  42. 60. That gives us what portion of the circle it
  43. is. And then times two pi r, which gives us
  44. the circumference.
  45. Sure. Okay, there's another arc, the Arc de Triomphe in
  46. Paris. Okay, so here's an example, So mm of a
  47. C equals what m of a D.
  48. C equals what?
  49. And then length of a C equals what length of
  50. a D.
  51. C equals what, cause me.
  52. See if you can figure this out on your own
  53. and then come back to me.
  54. Okay, here's the answers.
  55. The minor arc A.
  56. C is 84 degrees.
  57. The major arc would be 3 60 minus 84 which
  58. is to 76.
  59. And then to find the length of a C, we
  60. would do its degrees 84 divided by 3 60 times
  61. two pi times 77 is the radius, which equals 10.26
  62. centimeters. And then the big arc would be its degrees
  63. to 76/3, 60 times two pi seven Because seven is
  64. still the radius equals 33.72.
  65. Mhm. Alright, a horseshoe.
  66. Is that a narc?
  67. All right, here's another example.
  68. So X Y is 180 degrees because it's half a
  69. circle. Find the length of X Y if the radius
  70. is 11, so cause me, see if you can come
  71. up with it.
  72. All right, here's the answer.
  73. So the formula is 180 degrees, divided by 3, 60
  74. times. Two times pi times 11 equals 34.56 Okay, let
  75. me tell you a secret.
  76. I actually don't divide until the end.
  77. I do the whole top part first.
  78. I do 1 80 times, two times pi times 11
  79. and then divide by 3 60.
  80. Because it's all multiplication and division.
  81. You can do that.
  82. Okay, here's another arc from Arches National Forest.
  83. Okay, try this one.
  84. So the measure of X Y is 90 degrees by
  85. the length.
  86. If the radius is 11, cause me and come back
  87. to me to see if you're correct.
  88. All right, so we do 90 divided by 3.
  89. 60 is two times pi times 11, which equals 17.28
  90. millimeter. Were you right?
  91. Okay, here's another picture from Arches National Park.
  92. All right, try this one.
  93. If the measure of X Y is 120 degrees and
  94. the radio says 11, find the length of X Y
  95. yl. Right?
  96. Hopefully you got 23.4 e.
  97. This garden is in the guy.
  98. Have a word problem for you regarding a garden.
  99. So it's about the garden has a diameter of 20
  100. ft. If I want to plant 12 groups of flowers
  101. in equal lengths around the garden, how many feet of
  102. each type of flower would I need?
  103. Pause me and see if you can figure this out.
  104. Okay. So what I did is I took 360 divided
  105. by 12 because I wanted 12 sections of the flowers
  106. that equals 30 degrees.
  107. So each portion would be 30 degrees, and so each
  108. arc would measure 30 degrees.
  109. So then you take that 30 degrees, divided by 3,
  110. 60 times.
  111. Two times pi times 20 equals 10.47 Did anyone catch
  112. that? I just made a mistake there.
  113. Okay, I'm gonna give you double extra credit if you
  114. see what my mistake is not going to tell you
  115. what it was, but there's a mistake there.
  116. Yeah, here's the Talladega Raceway That has arcs in it.
  117. So I have a raceway problem for you.
  118. Okay, so each length unit on this speedway diagram represents
  119. 1/10 of a mile.
  120. So in other words, the three equals 30.3 miles and
  121. the three is the radius.
  122. What's the length of the entire track in miles?
  123. Pause me.
  124. See if you can figure this out.
  125. All right.
  126. So first we find the arc length of the part
  127. around angle A and so we would do 90 divided
  128. by 3.
  129. 60 times.
  130. Two times.
  131. Pi times three, which is 4.71 Next, we to find
  132. the arc length around angle B.
  133. So we do.
  134. 102 divided by 3.
  135. 60 times two Times Pi Times three, which equals 5.34
  136. Okay, then we find the length of the track around
  137. Angle C, which is 1 38 divided by 3 60
  138. times two times Pi times three, which is 7.23 All
  139. right, so we got through all three arcs.
  140. 7.23 plus 5.34 plus 4.71 and we add it to
  141. the three lengths that we have +56 and eight.
  142. We get 36.28 and then, since each unit equals 1/10
  143. we divide by 10.
  144. Eso 36.28 divided by 10 is 3.6 to 8 miles
  145. around the track.
  146. Did you get that?
  147. All right, here is where I'm at in 1959 a
  148. 15 year old boy named Jim, but 2.5 acres of
  149. land in southern Colorado for $450 he began building a
  150. cabin out of the stones on the land before, along
  151. the cabin grew toe look like a castle, he continued
  152. building for 40 years.
  153. The castle is now three stories high, with a ballroom
  154. and towers and bridges and a fire breathing dragon.
  155. If you saw the dragon is right behind me.
  156. Jim believed in having a dream.
  157. And if you stick to your dream and believe in
  158. yourself, anything can happen.
  159. All right.
  160. Thanks for sticking with me and have a fantastic day.