How to Measure the Arc or Central Angle

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Measuring the arc or central angle will require you to find the circum center. Measure the arc or central angle with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hello. My name is Walter Unglaub, and this is how to measure the arc or central angle. Well, an arc is just a segment of a circle and the central angle is the angle that that arcs of 10s based off of the center of the circle or a circum center. The way we can develop a relationship between the arc or the central angle is to consider the total possible angle and arc length. We know that the circumference of a circle, c is equal to 2 Pi r, where r is our radius and we know that the total angle for the entire circle theta sub t is equal to 360 degrees, which is equal 2 Pi radians. So we can use this information to derive an expression that relates the arc and central angle in terms of ratios. So given an angle theta that is less than 2 Pi, I'll also have an arc length that is less than the circumference. So what I can simply do is have my angle over the total possible angle and that ratio will be equal to the arc length which are the note as s divided the circumference. So plugging in what I know about the circle I'm going to have theta, the central angle divided by 2 Pi and my arc length divided by 2 Pi r. So notice that the 2 Pis will cancel out, so I'm left with the length of the arc is equal to the radius times that angle, where that angle is being measured in radians. Alternatively I could have considered degrees where I would have my angle measured in degrees divided by 360 and then my arc length here would be divided by the circumference which is 2 Pi r and if I use degrees to measure my angle then my arc length would be equal to 2 Pi r theta divided 360 which is equal to Pi r theta divided 180. So these are two equivalent expressions that relate the arc length and the central angle, one in terms of radians and the other in terms of degrees. So given one piece of information one can calculate the other using one of these two equivalent expressions. My name is Walter Unglaub and this is how to measure the arc or central angle.


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