What is the Difference Between Arc Measure and Arc Length?
🆚 Go to Comparative Table 🆚The difference between arc measure and arc length lies in the way they are measured and their units of measurement.
- Arc measure is a measurement of an arc using the angle that it makes at the center of the circle. It is measured in degrees or radians and represents the angle subtended by the arc at the center of the circle. The arc measure of an arc is also known as the angle measure of an arc.
- Arc length is a measurement of an arc using its actual length, which is the distance along the curve from the starting to the endpoint. Arc length is measured in units of length, such as centimeters, meters, or feet. The relation between the arc length (S) and the angle measure of the arc (θ) is given by the formula S = rθ, where r is the radius of the circle and θ is the angle measure of the arc in radians.
In summary, arc measure is the angle subtended by an arc at the center of the circle, while arc length is the actual distance along the curve of the arc.
On this pageWhat is the Difference Between Arc Measure and Arc Length? Comparative Table: Arc Measure vs Arc Length
Comparative Table: Arc Measure vs Arc Length
The main difference between arc measure and arc length lies in what they represent and how they are measured. Here is a table comparing the two:
| Feature | Arc Measure | Arc Length |
|---|---|---|
| Definition | Arc measure is the angle an arc makes at the center of its circle. | Arc length is the distance along an arc measured in linear units (e.g., inches, cm, m). |
| Measurement | Arc measure is measured in degrees or radians. | Arc length is measured in units of length. |
| Symbol | Arc measure is represented as $$\theta$$ radians or $$\theta$$ degrees. | Arc length is represented as $$s$$. |
| Relationship | The relationship between arc length and arc measure is given by the formula: $$s = r\theta$$, where $$s$$ is the arc length, $$r$$ is the radius, and $$\theta$$ is the angle measure of the arc in radians. | The relationship between arc length and arc measure can be expressed using the formula: $$s = r\theta$$, where $$s$$ is the arc length, $$r$$ is the radius, and $$\theta$$ is the angle measure of the arc in radians. |
Remember not to confuse arc measurements with the straight-line distance of a chord. The chord's length will always be shorter than the arc's length.
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