Determining an Arc in Geometry

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Determining an arc in geometry will either measure the arc in degrees or length in distance, depending on the situation. Determine an arc in geometry with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Math Calculations
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Video Transcript

Hi, I'm Drew Moyer, and this is how to determine an arc in geometry. Determining an arc in geometry can mean one or two things which is either the arc measure in degrees or the arc length in distance, inches, feet, anything like that and they can both be solved in the same way when given one or the other. Suppose we have circle A with arc B, C which has a measure of 60 degrees and a radius of six inches. Since I know that I want to find out how long B, C is, I know it must be a portion of the entire circumference just as 60 degrees is a portion of the whole circle, 360 degrees. So I can set up a proportion to solve for X and I will do 60/360 which is the part that the sector is to the whole circle is equal to arc B, C which I will abbreviate with X is to the whole circumference. So, 60/360 equals X/circumference which is 2Pi R. So 2 times Pi times 6. And then I would simplify that further, 60/360 is equal to X/12 Pi. And I can simplify this further because I know 60/360 would abbreviate to 1/6. So 1/6 equals X/12 Pi and then I would just cross multiply and I would get 6X equals 12 Pi, divide both sides by 6, X equals 2 Pi and then I could simplify that by putting in 3.14 for Pi and I get that X is equal to approximately 6.28 inches. I'm Drew Moyer, and this is determining an arc in geometry.


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