the myrtle beach skywheel has:\nmiddle height: 102 feet\nradius: 85 feet\na person starts at the bottom of…

the myrtle beach skywheel has:\nmiddle height: 102 feet\nradius: 85 feet\na person starts at the bottom of the wheel. the\nwheel then turns counterclockwise.\ncomplete the table with the very precise\nestimates of the persons height after each amount\nof turn.\nhint: your answer for a 60 degrees turn is in the\nfirst row.\nto get the answer you typed\n85 sin(60 + 270) + 102 in the calculator.\n

the myrtle beach skywheel has:\nmiddle height: 102 feet\nradius: 85 feet\na person starts at the bottom of the wheel. the\nwheel then turns counterclockwise.\ncomplete the table with the very precise\nestimates of the persons height after each amount\nof turn.\nhint: your answer for a 60 degrees turn is in the\nfirst row.\nto get the answer you typed\n85 sin(60 + 270) + 102 in the calculator.\n

Answer

Answer:

For (80^{\circ}): (85\sin(80 + 270)+102=85\sin(350)+102\approx85\times(- 0.1736)+102=-14.756 + 102 = 87.244)

For (160^{\circ}): (85\sin(160+270)+102=85\sin(430)+102=85\sin(430 - 360)+102=85\sin(70)+102\approx85\times0.9397+102 = 80.8745+102=182.8745)

For (200^{\circ}): (85\sin(200 + 270)+102=85\sin(470)+102=85\sin(470-360)+102=85\sin(110)+102\approx85\times0.9397+102 = 80.8745+102 = 182.8745)

For (410^{\circ}): (85\sin(410+270)+102=85\sin(680)+102=85\sin(680 - 2\times360)+102=85\sin(-40)+102\approx85\times(-0.6428)+102=-54.638+102 = 47.362)

Explanation:

Step1: Use the formula (h = r\sin(\theta + 270)+H)

Here (r = 85) (radius), (H=102) (middle - height), and (\theta) is the degrees turned.

Step2: Calculate for each (\theta)

  • For (\theta = 80^{\circ}): (\theta+270=350^{\circ}), (\sin(350^{\circ})\approx - 0.1736), (h = 85\times(-0.1736)+102)
  • For (\theta = 160^{\circ}): (\theta + 270=430^{\circ}), (\sin(430^{\circ})=\sin(430 - 360)=\sin(70^{\circ})\approx0.9397), (h = 85\times0.9397+102)
  • For (\theta = 200^{\circ}): (\theta+270 = 470^{\circ}), (\sin(470^{\circ})=\sin(470 - 360)=\sin(110^{\circ})\approx0.9397), (h=85\times0.9397 + 102)
  • For (\theta = 410^{\circ}): (\theta+270=680^{\circ}), (\sin(680^{\circ})=\sin(680-2\times360)=\sin(-40^{\circ})\approx - 0.6428), (h=85\times(-0.6428)+102)