# 8.4: Arc Length

**At Grade**Created by: CK-12

## Learning Objectives

- Calculate the length of an arc of a circle.

## Arc Length

Arcs are measured in two different ways:

**Degree measure:** The degree measure of an arc is the fractional part of a complete circle that the arc is.

**Linear measure:** This is the length, in units such as centimeters and feet, if you traveled from one end of the arc to the other end.

- Arcs can be measured in __________ ways, _____________________________ measure and ___________________________ measure.

**Example 1**

*Find the length of if . The radius of the circle is 9 inches.*

Remember, is the measure of the **central angle** associated with . This is the **degree measure** of the arc.

To find the **linear measure** of the arc, or , we use the fact that it is of an entire circle.

The circumference of the circle is:

The length of the arc, in this case, is of the entire circumference of the circle.

The **arc length** of is: inches or 9.42 inches

In this lesson we study the second type of arc measure—the **linear measure** of an arc, or the arc’s length. **Arc length** is directly related to the **degree measure** of an arc.

Suppose a circle has:

- circumference
- diameter
- radius

Also, suppose an **arc** of the circle has degree measure .

Realize that is the fractional part of the circle that the arc represents.

**Arc length**

**Reading Check:**

1. *In your own words, describe the linear measure of an arc:*

2. *True/False:* The **degree measure** of an arc is exactly the same as the **linear measure** of an arc.

3. *How could you correct the statement in #2 above to make it true?*

4. *Why do we use the fraction to calculate arc length? Describe.*

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