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!
More Answers:
Understanding Arcs in Geometry: Measures, Calculations, and ApplicationsCalculating Circumference and Area of Semicircles: Formulas and Explanation
Understanding Minor Arcs in Mathematics: Definition and Examples