Question

texas star ferris wheel
on the previous slide you placed the purple point in place where a person will be after:
they enter the wheel at the bottom
the wheel turns 55 degrees
the texas star has:
middle height: 106 feet
radius: 101 feet
type a very precise estimate of the height of the purple point.
(hint: use degrees standard from the circle)
feedback:
attempts: 0

Explanation:

Step1: Determine the formula for height

The height \(h\) of a point on a Ferris - wheel is given by the formula \(h = r\sin\theta+h_{0}\), where \(r\) is the radius, \(\theta\) is the angle in standard position, and \(h_{0}\) is the middle - height.
The middle - height \(h_{0}=106\) feet and the radius \(r = 101\) feet. The angle \(\theta=55^{\circ}+ 270^{\circ}=325^{\circ}\).

Step2: Calculate \(\sin\theta\)

We know that \(\sin(325^{\circ})=\sin(360^{\circ}-35^{\circ})=-\sin(35^{\circ})\). Using a calculator, \(\sin(35^{\circ})\approx0.5736\), so \(\sin(325^{\circ})\approx - 0.5736\).

Step3: Calculate the height

Substitute \(r = 101\), \(h_{0}=106\), and \(\sin\theta\approx - 0.5736\) into the formula \(h=r\sin\theta + h_{0}\).

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Answer:

$151.8$ feet