texas star ferris wheel\non the previous slide you placed the purple point in place where a person will be…

texas star ferris wheel\non the previous slide you placed the purple point in place where a person will be after:\nthey enter the wheel at the bottom\nthe wheel turns 55 degrees\nthe texas star has:\nmiddle height: 106 feet\nradius: 101 feet\ntype a very precise estimate of the height of the purple point.\n(hint: use degrees standard from the circle)\nfeedback:\nattempts: 0

texas star ferris wheel\non the previous slide you placed the purple point in place where a person will be after:\nthey enter the wheel at the bottom\nthe wheel turns 55 degrees\nthe texas star has:\nmiddle height: 106 feet\nradius: 101 feet\ntype a very precise estimate of the height of the purple point.\n(hint: use degrees standard from the circle)\nfeedback:\nattempts: 0

Answer

Answer:

$151.8$ feet

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}). [ \begin{align*} h&=101\times(-0.5736)+106\ &=-57.9336 + 106\ &=48.0664\approx151.8 \end{align*} ]