Question

Kristin boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for one full rotation. The radius of the Ferris wheel is 8 meters. Imagine an angle with a vertex at the center of the Ferris wheel that subtends the arc along which Kristin travels.If Kristin travels 10.4 meters, what is the angle's measure in radians? radians   If Kristin travels 24.8 meters, what is the angles' measure in radians? radians   Let s represent the varying number of meters that Kristin has traveled since the Ferris wheel started rotating. Write an expression that represents the varying measure of the angle (in radians).   

Answer 1

The Arc Length

Given a circle of radius r, the arc length, or the distance between two points along the circle that has a central angle of θ, is given by:

S = θ.r

The angle θ must be expressed in radians.

We are given the radius of the Ferris wheel of r=8 m and the distance (arc length) that Kristin travels of S=10.4 meters. We can calculate the central angle in radians solving for θ:

$\theta=\frac{S}{r}$

Substituting:

$\theta=\frac{10.4}{8}=1.3$

The angle's measure is 1.3 radians.

Now we are required to find the angle when Kristin travels S=24.8 meters.

$\theta=\frac{24.8}{8}=3.1$

The angle is 3.1 radians.

If we were given different measures of S, the central angle, in radians, can be calculated by the expression:

$\theta=\frac{S}{8}$