Calculating the Length of an Arc: A Step-by-Step Guide

Arc of a circle

The arc of a circle is a portion of the circumference of the circle

The arc of a circle is a portion of the circumference of the circle. It is a curved segment that connects two points on the circumference of the circle. The length of the arc is measured along the circumference and can be calculated using the formula:

Arc length = (θ/360) × 2πr

Where:
– θ is the central angle of the arc in degrees
– r is the radius of the circle

To explain the formula, if you imagine a full circle, it has 360 degrees. So, if you have a central angle θ that is less than 360 degrees, the arc’s length will be proportional to the fraction (θ/360) of the full circumference of the circle.

For example, let’s say we have a circle with a radius of 5 units and a central angle of 60 degrees. To find the arc length, we can use the formula:

Arc length = (60/360) × 2π(5)
Arc length = (1/6) × 10π
Arc length = 10π/6
Arc length ≈ 5.24 units

So, the length of the arc with a 60-degree central angle on a circle with a radius of 5 units is approximately 5.24 units.

It’s worth noting that if the central angle is 360 degrees or the arc spans the full circumference, then the arc length will be equal to the circumference of the circle, which is 2πr.

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