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?

Additional Topics in MathCongruence and similarity
Product TypeSAT Math
SATSAT Math
SAT MathAdditional Topics in Math
Geometry and Measurement
Test PrepSAT Math

Transcript

00:19

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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more participation trophies for you Start with the angle here

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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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radiance so they're always going to give you answers here

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That might seem logical on the way back part of 00:02:12.53 --> [endTime] your brain but aren't