The car in the figure below travels a distance of 745 m along the track, and the driver finds that she has traveled through an angle of 475°. What is the radius of the track?
To find the radius of the track, we can use the relationship between the angle traveled and the arc length. The formula is:
arc length = radius * angle in radians
First, let's convert the angle from degrees to radians. Since there are 360 degrees in a circle and 2π radians, we can convert by multiplying the angle by π/180:
angle in radians = 475° * (π/180) ≈ 8.29 radians
Next, we can rearrange the formula to solve for the radius:
radius = arc length / angle in radians
Given that the arc length is 745 m, we can substitute the values into the equation:
radius = 745 m / 8.29 radians ≈ 89.85 m
Therefore, the radius of the track is approximately 89.85 meters.