# SAT Math: Calculating Arc Length Using Proportions

A circle has a radius of 6 and a central angle ∠XYZ that measures . What is the length of the major arc formed by the central angle?

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here It's gonna look like this I'm here to here's

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to forty And then we got to X and line

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Zeke And yes how rude it was of this problem

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to not come with a drawing Yeah you have to

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make one sometimes but that's because we're in America No

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of four pi over three and converted to degrees We

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had for pirating ins over three times the hundred degrees

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over pi radiance That's how we got to two Forty

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They're spinning counterclockwise Okay And this is how big the

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central angle in the circle has to be This thing

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which is a pretty big to forty big number Imagine

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having to run around the circle to get from X

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to Z by taking the longer route Well that's the

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root of the major ark We need to measure and

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to find the distance around a part of the circle

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First find the distance around the full circle which is

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the What's it called Oh yes Circumference Well the problem

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says the radius is six and the circumference is always

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two Pi r Right That's just by definition So sir

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Come sir Go to buy our equals two high times

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six which is twelve Pie Got it Simple That's the

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circumference Well given the circumference here we can measure the

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art by setting up a proportion We need to measure

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the arc length created by two hundred forty degree arc

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out of the full circle Three Sixty measure So what

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is that Well we got to forty over three Sixty

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There equals that arc x z over twelve pie because

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that's a circumference right That's the three sixty Think so

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reduces down to two thirds equals xy over twelve pie

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Or send another way If we divide the numbers out

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here we get well the ark XY is just a

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pie So the length of the major arc X Z

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formed by the central angle is a pirate's answer See

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and remember this is a distance of the long way

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From ecstasy not the short way which is for pie

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They throw that curve ball like you There'd be and

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twelve five's The total circumference on a portion of it

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into pie is the full angle of a circle and

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