Question

A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.

Answer 1

central angle/360 = arc length/2pi•r

Let π = pi

Let A = length of intercepted arc

45/360 = A/2(20)π

1/8 = A/40π

8A = 40π

A = 40π/8

A = 5π

Did you follow?

Answer 2

The length of the arc is 5π inches

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