Shelly and Jamie participate in a street relay race. Jamie must run from point B along AB⌢, which represents part of a roundabout, to pass off the baton to Shelly at point A. If the central angle measures 123∘, and the radius of the roundabout is 50 meters, how many meters must Jamie sprint to reach Shelly?
Use π≈3.14 and round your answer to the nearest meter.
To calculate the distance Jamie must sprint, we first need to find the arc length AB⌢.
The formula to find the arc length of a circle is:
Arc Length = (θ/360) x 2πr
where θ is the central angle and r is the radius of the circle.
Plugging in the values:
Arc Length = (123/360) x 2 x 3.14 x 50
Arc Length = (0.3417) x 314
Arc Length ≈ 107.1 meters
Therefore, Jamie must sprint approximately 107 meters to reach Shelly.