Calculating Arc Length: A Step-by-Step Guide with Formula and Example

Arc

Arc refers to a portion of the circumference of a circle

Arc refers to a portion of the circumference of a circle. It is a curved part of a curve or a circle that spans two endpoints on the curve. The length of an arc is defined as the distance along the curve between these two endpoints.

To calculate the length of an arc, you need to know the measure of the central angle (θ) that subtends the arc and the radius (r) of the circle.

The formula to find the length of an arc is given by:

Arc Length = (θ/360) * 2πr

Where:
– θ is the measure of the central angle in degrees.
– π (pi) is a constant approximately equal to 3.14159.
– r is the radius of the circle.

To use this formula, follow these steps:

1. Ensure that the central angle (θ) is measured in degrees and the radius (r) is measured in the same units as the length you desire (e.g., centimeters, inches).

2. Convert the central angle measurement to degrees, if necessary. If the angle is already in degrees, you can skip this step.

3. Plug the values of θ and r into the formula for arc length.

4. Perform the calculations using the order of operations (parentheses, exponents, multiplication/division, addition/subtraction).

5. Round the result to the appropriate number of decimal places, depending on the level of precision required.

Let’s illustrate this with an example:

Suppose we have a circle with a radius of 5 inches, and we want to find the length of the arc subtended by a central angle of 60 degrees.

Using the formula: Arc Length = (θ/360) * 2πr

Substituting the given values:
Arc Length = (60/360) * 2 * π * 5

Simplifying:
Arc Length = (1/6) * 2 * 3.14159 * 5
Arc Length = (1/6) * 31.4159
Arc Length ≈ 5.23598 inches

Therefore, the length of the arc with a central angle of 60 degrees in a circle with a radius of 5 inches is approximately 5.236 inches.

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