Answer:
[tex]Angle\ of\ rotation \approx 19.35\textdegree[/tex]
Step-by-step explanation:
[tex]Diameter\ of\ the\ wheel=225\ feet\\\\Radius=\frac{diameter}{2}=\frac{225}{2}=112.5\ feet\\\\Central\ angle(radians)=\frac{arc\ length}{radius}\\\\Angle=\frac{38}{112.5}\\\\Angle=0.337778\ radians[/tex]
Convert the angle in degrees
[tex]\theta (degree)=\phi (radians)\times \frac{180}{\pi}[/tex]
[tex]Angle=0.337778\times \frac{180}{\pi}\\\\Angle\approx 19.35\textdegree[/tex]
When the wheel stops to let more passengers on, the angle of rotation is 19.35 degrees.
A Ferris wheel has a diameter of 225 feet.
If a passenger gets in a car and travels 38 feet when the wheel stops to let more passengers on.
The angle of rotation.
A Ferris wheel has a diameter of 225 feet.
If a passenger gets in a car and travels 38 feet when the wheel stops to let more passengers on.
The radius is of the wheel is,
[tex]\rm Radius = \dfrac{diameter}{2}\\\\Radius = \dfrac{225}{2}\\\\Radius = 112.5 \ feet[/tex]
The angle of rotation is determined by the following formula,
[tex]\rm Central \ angle = \dfrac{Arc \length}{radius}[/tex]
Substitute all the values in the formula
[tex]\rm Central \ angle = \dfrac{Arc \length}{radius}\\\\\rm Central \ angle = \dfrac{38}{112.5}\\\\Central \ angle = 0.33 \ radian[/tex]
Converting the angle into the degree,
[tex]\rm = 0.33 \times \dfrac{180}{\pi }\\\\=19.35 \ degree[/tex]
Hence, The angle of rotation is 19.35 degrees.
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