Question

If the arc of a circle is 15 meters long and the radius of the circle is 3 meters, then what is the measure of the central angle, to the nearest tenth of a degree, that intercepts that 15-meter arc?

Answer 1

To find the measure of the central angle, first calculate the circumference of the circle using the formula C = 2πr, where r is the radius of the circle.

C = 2π(3)
C = 6π ≈ 18.85 meters

Next, since the arc length is 15 meters and the circumference of the circle is 18.85 meters, you can find the central angle using the formula:

Central angle = (arc length / circumference) * 360

Central angle = (15 / 18.85) * 360
Central angle ≈ 286.92 degrees

Therefore, the measure of the central angle that intercepts the 15-meter arc is approximately 286.9 degrees.