Arc Length Formula
The arc length formula is used to calculate the length of an arc on a circle
The arc length formula is used to calculate the length of an arc on a circle. To understand the formula, let’s first define some terms:
– Arc Length: The distance along a part of the circumference of a circle.
– Radius: The distance from the center of the circle to any point on the circumference.
– Central Angle: The angle formed by two radii drawn to the two endpoints of an arc, with the center of the circle as the vertex.
The formula for calculating arc length is:
Arc Length = (Central Angle / 360) * (2 * π * Radius)
In this formula, we divide the central angle by 360 to find the proportion of the circle it represents. Then, we multiply this proportion by the circumference of the entire circle (2 * π * Radius) to find the length of the arc.
Let’s look at an example to better understand how to use this formula:
Example: Find the arc length of a circle with a radius of 5 units and a central angle of 120 degrees.
1. First, calculate the proportion of the circle represented by the central angle:
Proportion = Central Angle / 360 = 120 / 360 = 1/3
2. Next, find the circumference of the circle:
Circumference = 2 * π * Radius = 2 * π * 5 = 10π
3. Finally, calculate the arc length by multiplying the proportion by the circumference:
Arc Length = Proportion * Circumference = (1/3) * (10π) = (10/3)π
Therefore, the arc length of the circle with a radius of 5 units and a central angle of 120 degrees is (10/3)π units.
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