In Try This 4 you may have identified the relationship between arc length, radius, and central angle:
arc length = central angle in radians × radius of the circle
Using variables, this expression can be written as a = θr, where
Read “Arc Length of a Circle” on page 173 of the textbook to learn more about why arc length can be determined using the formula a = θr.
In Try This 3 you determined how far the horse walked, or the arc length for a partial rotation around a circle. In Try This 4 you found the relationship between the length of an arc, radius, and central angle. In Try This 5 you will try to calculate the length of an arc when you know the central angle and radius of the circle.
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A baseball diamond can be thought of as part of a circle. At home plate, the central angle is 90° and the radius of the circle is 72 m, as shown in the diagram. Jane needs to build a fence around the outfield of a baseball diamond. The fence will follow the arc of the circle.
Determine the length of the fence Jane needs to build. Explain your process.
Save your response in your course folder.