## arc length

### In geometry, an arc length refers to the length of a portion of a curve

In geometry, an arc length refers to the length of a portion of a curve. More specifically, it is the distance along the curve between two specified points. Arc lengths are commonly measured in units such as centimeters or inches.

To find the arc length, we can use the formula:

Arc Length = θ * r

where θ is the angle (in radians) subtended by the arc at the center of the circle, and r is the radius of the circle.

However, if we are dealing with a portion of a circle rather than a full circle, we modify the formula above by using the fraction of the circumference of the circle that the arc represents:

Arc Length = (θ/2π) * 2πr

where 2πr represents the circumference of the circle.

Additionally, if we are given the angle in degrees rather than radians, we need to convert it to radians by using the formula:

θ (in radians) = (π/180) * θ (in degrees)

Let’s consider an example to better understand how to find the arc length. Suppose we have a circle with a radius of 5cm, and we want to find the arc length of a portion of the circle subtended by a central angle of 60 degrees. We can use the following steps:

1. Convert the angle from degrees to radians:

θ (in radians) = (π/180) * 60 = π/3 radians

2. Plug the values into the arc length formula:

Arc Length = (θ/2π) * 2πr = ((π/3)/(2π)) * (2π * 5) = 5 cm

Therefore, the arc length of the given portion of the circle is 5 cm.

Remember, the arc length is always a linear measurement along the curve, and it is dependent on both the angle subtended and the radius of the circle.

##### More Answers:

Understanding Circumscribed Polygons and Their Geometric PropertiesFinding the Measure of a Central Angle in a Circle | Formula and Example Calculation

The Complete Guide to Understanding and Working with Circles in Mathematics | Properties, Concepts, and Formulas