anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1442538379561:dw|
johnweldon1993
  • johnweldon1993
Well 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
  • anonymous
18

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anonymous
  • anonymous
what do you mean by the angle in radian?
anonymous
  • anonymous
Can you tell me what they mean when they say "An inscribed angle is aways half the central angel."
johnweldon1993
  • johnweldon1993
Okay 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
  • johnweldon1993
|dw:1442584881833:dw|
johnweldon1993
  • johnweldon1993
|dw:1442584923535:dw|
anonymous
  • anonymous
ohhhhh
johnweldon1993
  • johnweldon1993
The inscribed angle *According to the Cenntal Angle Theorem* is always equal to HALF the central angle
anonymous
  • anonymous
what does that mean?
johnweldon1993
  • johnweldon1993
SO 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
  • anonymous
i've never seen that 0 thing before.
johnweldon1993
  • johnweldon1993
\(\large \theta\) = theta = a measure of an angle :)
anonymous
  • anonymous
oh ok
johnweldon1993
  • johnweldon1993
yeah lol sorry :D Okay so...lets look at your circle |dw:1442585177036:dw|
johnweldon1993
  • johnweldon1993
Comparing that to my circle I drew above, it looks like you have the INSCRIBED angle labeled here right? |dw:1442585225131:dw|
johnweldon1993
  • johnweldon1993
SO...since that formula \[\large s = r\theta\] Requires the CENTRAL angle...and we have the inscribed...what would be the central angle?
anonymous
  • anonymous
|dw:1442585190505:dw|
johnweldon1993
  • johnweldon1993
Not 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
  • anonymous
the inscribed angle looks bigger than the central angle why is it only half the central angle?
johnweldon1993
  • johnweldon1993
It looks bigger?|dw:1442585541996:dw|
anonymous
  • anonymous
ohhhhh okay i see
johnweldon1993
  • johnweldon1993
Idk if that helped...or made it more confusing...
johnweldon1993
  • johnweldon1993
Okay good lol
johnweldon1993
  • johnweldon1993
So yeah...look back up to my formula up there...Does it make sense? \[\large s = r\theta\] \[\large s = 18 \times (80 \times \frac{\pi}{180})\]
anonymous
  • anonymous
yes
johnweldon1993
  • johnweldon1993
Perfect, 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
anonymous
  • anonymous
2pi is 360 degrees?
johnweldon1993
  • johnweldon1993
Indeed |dw:1442585940253:dw|
johnweldon1993
  • johnweldon1993
Remember a whole circle is 360 degrees right?
johnweldon1993
  • johnweldon1993
If we travel pi units around the circle...we travel halfway around it...or half of the 360 which is 180
johnweldon1993
  • johnweldon1993
If we then travel another pi units around....2pi....we have traveled around the whole circle...or 360 degrees
anonymous
  • anonymous
ohhhhh
johnweldon1993
  • johnweldon1993
Alright 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
  • anonymous
|dw:1442586054554:dw|
johnweldon1993
  • johnweldon1993
Where is that 36pi term coming from?
anonymous
  • anonymous
|dw:1442586190316:dw|
anonymous
  • anonymous
36 pi is from the diameter
anonymous
  • anonymous
which is the circumference of the whole circle
anonymous
  • anonymous
i subtracted the circumference from the central angle
anonymous
  • anonymous
Is arc ABC the same as arc AC
johnweldon1993
  • johnweldon1993
Well now the only thing is The want the length of arc ABC |dw:1442586432497:dw|
anonymous
  • anonymous
|dw:1442586538130:dw|
johnweldon1993
  • johnweldon1993
So we found that length already...the 8pi By subtracting the 8pi from the whole circumference...we are actually getting |dw:1442586574680:dw|
anonymous
  • anonymous
Yea i think that's what they wanted
anonymous
  • anonymous
Is there a reason we have to find the central angle to find the arc length? Couldnt we have found it using the inscribed angle?
anonymous
  • anonymous
@johnweldon1993

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