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.

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

Jamie must sprint 107 meter to pass Shelly at point A.

Explanation:

Circumference of a sector of the circle is represented by,

Circumference =
`(\theta)/(360)(2\pi r)`

where θ = central angle subtended at the center by an arc

r = radius of the circle

`m(\widehat{AB})` =
`(123)/(360)(2\pi )(50)`

= 34.1667π

= 107.34 meter

≈ 107 meter

Therefore, Jamie must sprint 107 meter to pass Shelly at point A.