Question

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.

Points A and B lie on a circular path representing a roundabout. Point C is the center of the circular roundabout.


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.

Enter your answer as a number, like this: 42

Answer 1

Distance Jamie must sprint to reach Shelly is; L = 107 m

Explanation:

We are given;

Central angle;θ = 123°

Radius;r = 50m

Now, for us to find out how many meters Jamie must sprint to reach Shelly, we'll use the formula for arc length of a circle;

Arc length; L = 2πr(θ/360)

So, plugging in the relevant values, we have;

L = 2π(50)(123/360)

L = 107.34 ≈ 107 m

L = 107 m