Answer:
The length of the arc is 5π inches
Step-by-step explanation:
* Lets explain the relation between the central angle and its
intercepted arc
- If the vertex of an angle is the center of the circle and the two sides
of the angle are radii in the circle, then this angle is called a
central angle
- Each central angle subtended by the opposite arc, the name of the
arc is the starting point and the ending point of the angle
- There is 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 depends on the measure of its
central angle and the length of the radius and the measure of the arc
- The measure of the circle is 360°
- The length of the circle is 2πr
- The length of the arc = central angle/360 × 2πr
* Now lets solve the problem
∵ The radius of the circle r = 20 inches
∵ The measure of the central angle is 45°
∵ The length of the arc = central angle/360 × 2πr
∴ The length of the arc = 45°/360° × 2 × π × 20 = 5π
* The length of the arc is 5π inches
