the texas star has: middle height: 106 feet radius: 101 feet a person starts at the bottom of the wheel. the…

Answer:

164

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

[ \begin{align*} h&=106 + 101(1-(- 0.3420))\ &=106+101\times(1 + 0.3420)\ &=106+101\times1.3420\ &=106 + 135.542\ &=164 \end{align*} ]