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anonymous
 one year ago
Help please....
If the diameter of the circle is 36, what is the length of arc ABC?
A. 8
B. 8pi
C. 28pi
D. 32pi
E. 56pi
anonymous
 one year ago
Help please.... If the diameter of the circle is 36, what is the length of arc ABC? A. 8 B. 8pi C. 28pi D. 32pi E. 56pi

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442538379561:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Well remember: \[\large s = r\theta\] The arc length is equal to the radius of the circle times the angle given in radians So first, what is the radius? And what is the angle in radians?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean by the angle in radian?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you tell me what they mean when they say "An inscribed angle is aways half the central angel."

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Okay hang on...lets go one by one lol...So first...the "inscribed angle is always half the central angle" Lets look at a circle

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442584881833:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1dw:1442584923535:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1The inscribed angle *According to the Cenntal Angle Theorem* is always equal to HALF the central angle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what does that mean?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1SO If we look again at that formula I gave you \[\large s = r\theta\] S = arc length *What we need r = radius of the circle \(\large \theta\) = the measure of the central angle in radians

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i've never seen that 0 thing before.

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \theta\) = theta = a measure of an angle :)

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1yeah lol sorry :D Okay so...lets look at your circle dw:1442585177036:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Comparing that to my circle I drew above, it looks like you have the INSCRIBED angle labeled here right? dw:1442585225131:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1SO...since that formula \[\large s = r\theta\] Requires the CENTRAL angle...and we have the inscribed...what would be the central angle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442585190505:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Not quite.. So if r = 18 remember And we have 80 degrees (because remember central is always double the inscribed) We have \[\large s = 18 \times (80 \times (\frac{\pi}{180}))\] \[\large s = 18 \times \frac{4\pi}{9}\] \[\large s = ?\] Does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the inscribed angle looks bigger than the central angle why is it only half the central angle?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1It looks bigger?dw:1442585541996:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Idk if that helped...or made it more confusing...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1So yeah...look back up to my formula up there...Does it make sense? \[\large s = r\theta\] \[\large s = 18 \times (80 \times \frac{\pi}{180})\]

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Perfect, Also I notice above you had \[\large \frac{{\pi}}{360}\] If you want to use 360 on the bottom...make sure you have 2pi on top...because remember 2pi is 360 degrees

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Indeed dw:1442585940253:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Remember a whole circle is 360 degrees right?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1If we travel pi units around the circle...we travel halfway around it...or half of the 360 which is 180

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1If we then travel another pi units around....2pi....we have traveled around the whole circle...or 360 degrees

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Alright cool, so now that we have that all clear simplify my equation down \[\large s = 18 \times (\frac{80\pi}{180})\] \[\large s = 18\times (\frac{4\pi}{9})\] \[\large s = 2\times 4\pi\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442586054554:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Where is that 36pi term coming from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442586190316:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.036 pi is from the diameter

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which is the circumference of the whole circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i subtracted the circumference from the central angle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is arc ABC the same as arc AC

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1Well now the only thing is The want the length of arc ABC dw:1442586432497:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442586538130:dw

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.1So we found that length already...the 8pi By subtracting the 8pi from the whole circumference...we are actually getting dw:1442586574680:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea i think that's what they wanted

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there a reason we have to find the central angle to find the arc length? Couldnt we have found it using the inscribed angle?
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