Question

the myrtle beach skywheel has:
middle height: 102 feet
radius: 85 feet
a person starts at the bottom of the wheel. the
wheel then turns counterclockwise.
complete the table with the very precise
estimates of the persons height after each amount
of turn.
hint: your answer for a 60 degrees turn is in the
first row.
to get the answer you typed
85 sin(60 + 270) + 102 in the calculator.

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 \(\theta = 410^{\circ}\):

\(\theta+270=680^{\circ}\), \(\sin(680^{\circ})=\sin(680-2\times360)=\sin(-40^{\circ})\approx - 0.6428\), \(h=85\times(-0.6428)+102\)

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