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 Math | Congruence and similarity |

Product Type | SAT Math |

SAT | SAT Math |

SAT Math | Additional Topics in Math Geometry and Measurement |

Test Prep | SAT Math |

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

to forty And then we got to X and line

Zeke And yes how rude it was of this problem

to not come with a drawing Yeah you have to

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

more participation trophies for you Start with the angle here

of four pi over three and converted to degrees We

had for pirating ins over three times the hundred degrees

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

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

central angle in the circle has to be This thing

which is a pretty big to forty big number Imagine

having to run around the circle to get from X

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

root of the major ark We need to measure and

to find the distance around a part of the circle

First find the distance around the full circle which is

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

says the radius is six and the circumference is always

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

Come sir Go to buy our equals two high times

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

circumference Well given the circumference here we can measure the

art by setting up a proportion We need to measure

the arc length created by two hundred forty degree arc

out of the full circle Three Sixty measure So what

is that Well we got to forty over three Sixty

There equals that arc x z over twelve pie because

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

reduces down to two thirds equals xy over twelve pie

Or send another way If we divide the numbers out

here we get well the ark XY is just a

pie So the length of the major arc X Z

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

and remember this is a distance of the long way

From ecstasy not the short way which is for pie

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

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

into pie is the full angle of a circle and

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

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