Question

Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. leave your answer in terms of π.

1. If the radius of the circle exists 2.4 kilometers and is intercepted by a central angle measuring 150° then the length of the arc exists 5π inches.

What was the relation between the central angle and its intercepted arc?

• If the vertex of an angle exists in the center of the circle and the two sides of the angle are radii in the circle, then this angle exists named a central angle.
• Each central angle exists subtended by the opposite arc, the name of the arc exists the starting point and the finish point of the angle.
• There exists a relation between the central angle and its subtended arc the measure of the central angle equals half the measure of its subtended arc.
• The length of the subtended arc relies on the measurement of its central angle and the length of the radius and the measure of the arc.
• The measurement of the circle exists at 360°.
• The length of the circle exists at 2πr.
The radius of the circle r = 2.4 kilometers
The measure of the central angle exists at 150°.
The length of the arc = central angle/360 × 2πr
The length of the arc = 150°/360° × 2 × π × 2.4 = 2π
The length of the arc exists 2π kilometers.