Question

the texas star has: middle height: 106 feet radius: 101 feet a person starts at the bottom of the wheel. the wheel then turns counterclockwise. complete the table with the very precise estimate of the persons height after the other amount of turn. degrees turned height (precise estimate) 55 48 110

Explanation:

Step1: Analyze the relationship

The height of a person on a Fer - ris wheel can be modeled by the formula \(h = h_0+r(1 - \cos\theta)\), where \(h_0\) is the middle height, \(r\) is the radius, and \(\theta\) is the angle of rotation.

Step2: Substitute the values

Given \(h_0 = 106\) feet, \(r=101\) feet, and \(\theta = 110^{\circ}\). First, convert the angle from degrees to radians: \(\theta = 110\times\frac{\pi}{180}=\frac{11\pi}{18}\) radians. Then use the formula \(h = 106+101(1-\cos(110^{\circ}))\). We know that \(\cos(110^{\circ})\approx - 0.3420\).

Step3: Calculate the height

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Answer:

164