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SAT Math: Calculating Arc Length Using Proportions 3 Views


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Description:

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?


Transcript

00:00

Yeah Whoa Okay Trig shmoop ear's A circle has a

00:06

radius of six and a central angle of X Y

00:09

Z That measures for pie over three radiance What's the

00:11

length of the major arc X Z formed by the

00:15

central angle All right so we gotta drive Little picture

00:19

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

00:22

to forty And then we got to X and line

00:24

Zeke And yes how rude it was of this problem

00:27

to not come with a drawing Yeah you have to

00:29

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

00:32

more participation trophies for you Start with the angle here

00:35

of four pi over three and converted to degrees We

00:39

had for pirating ins over three times the hundred degrees

00:42

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

00:44

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

00:48

central angle in the circle has to be This thing

00:51

which is a pretty big to forty big number Imagine

00:54

having to run around the circle to get from X

00:55

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

00:58

root of the major ark We need to measure and

01:00

to find the distance around a part of the circle

01:03

First find the distance around the full circle which is

01:05

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

01:08

says the radius is six and the circumference is always

01:11

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

01:14

Come sir Go to buy our equals two high times

01:17

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

01:20

circumference Well given the circumference here we can measure the

01:23

art by setting up a proportion We need to measure

01:25

the arc length created by two hundred forty degree arc

01:28

out of the full circle Three Sixty measure So what

01:31

is that Well we got to forty over three Sixty

01:33

There equals that arc x z over twelve pie because

01:37

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

01:40

reduces down to two thirds equals xy over twelve pie

01:43

Or send another way If we divide the numbers out

01:45

here we get well the ark XY is just a

01:48

pie So the length of the major arc X Z

01:51

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

01:54

and remember this is a distance of the long way

01:57

From ecstasy not the short way which is for pie

02:00

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

02:02

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

02:05

into pie is the full angle of a circle and

02:07

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

02:10

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

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