Question

you board a ferris wheel at ground level and travel to the very top, when it stops to allow more riders to get on. how many degrees has the ferris wheel rotated? 180° complete what is the radian equivalent for 180°? 2π radians π radians π/2 radians complete to the nearest foot, what is the radius of the ferris wheel if you traveled 157 feet? feet done

Explanation:

For the radius of the Ferris wheel problem:

Step1: Recall the arc length formula for a circle

The arc length \( s \) of a circle is given by \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians. We know the arc length \( s = 157 \) feet and the angle \( \theta=\pi \) radians (since the Ferris wheel rotated \( 180^\circ=\pi \) radians).

Step2: Solve for the radius \( r \)

From \( s = r\theta \), we can rearrange to get \( r=\frac{s}{\theta} \). Substituting \( s = 157 \) and \( \theta=\pi \approx 3.14 \), we have \( r=\frac{157}{3.14} \).

Step3: Calculate the value

\( \frac{157}{3.14} = 50 \).

Answer:

50