The Length of a Major Arc: Calculation and Example

Major arc

In mathematics, an arc is a portion of a curve which is part of the circumference of a circle

In mathematics, an arc is a portion of a curve which is part of the circumference of a circle. An arc is defined by two endpoints and the points lying on the curve between those endpoints. There are two types of arcs: minor arcs and major arcs.

A major arc is an arc that spans more than half of the circumference of a circle. In other words, if you were to extend the major arc to form a complete circle, it would be longer than a semicircle.

To calculate the length of a major arc, you need to know the circumference of the circle and the measure of the central angle that the arc subtends. The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius of the circle. The measure of the central angle is given in degrees.

To find the length of the major arc, you can use the formula:
Length = (central angle measure/360) * circumference

Let’s work through an example:
Suppose we have a circle with a radius of 5 units and a central angle measure of 120 degrees.

Step 1: Find the circumference of the circle.
C = 2πr = 2π(5) = 10π units

Step 2: Calculate the length of the major arc.
Length = (120/360) * (10π) = (1/3) * (10π) = (10/3)π units

Therefore, the length of the major arc in this example is (10/3)π units.

Remember to always work with the correct units, whether it’s in centimeters, inches, or any other unit of measurement that applies to your specific problem.

I hope this explanation helps you understand the concept of major arcs and how to calculate their lengths. If you have any further questions, feel free to ask!

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