JayDelV
  • JayDelV
What is the arc length of a circle that has a 7-centimeter radius and a central angle that is 40 degrees? Use 3.14 for π and round your answer to the nearest hundredth.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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arindameducationusc
  • arindameducationusc
theta=L/R
UsukiDoll
  • UsukiDoll
hmmm my textbook is like this though for arc length \[s = \theta r \]
arindameducationusc
  • arindameducationusc
where L = arc legth and r radius... Now I hope you can solve it.... if not, ask me

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More answers

UsukiDoll
  • UsukiDoll
s - arc length theta - the angle r - radius
UsukiDoll
  • UsukiDoll
I think we need to convert 40 degrees to radians \[40 \times \frac{\pi}{180} \rightarrow \frac{40 \pi}{180}\]
UsukiDoll
  • UsukiDoll
simplify that fraction first ^_^
arindameducationusc
  • arindameducationusc
Awesome @UsukiDoll Good job.. @JayDelV just follow @UsukiDoll
UsukiDoll
  • UsukiDoll
or we can reduce later.... \[s = \theta r \rightarrow s = \frac{40 \pi}{180} \times 7\]
JayDelV
  • JayDelV
I'm actually confused, sorry was eating.
UsukiDoll
  • UsukiDoll
you're looking for the arc length of a circle The arc length of a circle formula is \[s = \theta r \] where s - arc length theta - the angle r - radius we are given the angle which is 40 degrees, but it looks like we have to convert to radians so multiply 40 by \[\frac{\pi}{180} \] \[\frac{40 \pi}{180}\] this fraction is reducible. afterwards, multiply by 7 and you have your s which is the arc length
UsukiDoll
  • UsukiDoll
you were given an angle in degree mode. We can't use degree mode for this formula, so conversion to radians is necessary
UsukiDoll
  • UsukiDoll
it's best to reduce that fraction first.. otherwise you will be stuck with an even bigger fraction to reduce.
UsukiDoll
  • UsukiDoll
\[s = \theta r \rightarrow s =\frac{40 \pi}{180} \times 7 \rightarrow s = \frac{280 \pi}{180}\] now that's a monster fraction to be reduced.
UsukiDoll
  • UsukiDoll
what is 280 divided by 10 what is 180 divided by 10
JayDelV
  • JayDelV
28 and 18
UsukiDoll
  • UsukiDoll
ok.. we still need to reduce further \[s= \frac{28 \pi}{18}\] but this time by 2 what is 28 divided by 2 what is 18 divided by 2
JayDelV
  • JayDelV
14 and 9
UsukiDoll
  • UsukiDoll
yes so we have \[s= \frac{14 \pi}{9}\] we can't reduce anymore, so we got our arc length ;)
JayDelV
  • JayDelV
Thank you so much for your time I really appreciate it!
JayDelV
  • JayDelV
Oh wait, the answers are in decimals.
UsukiDoll
  • UsukiDoll
ah no problem we can convert to decimals XD
UsukiDoll
  • UsukiDoll
\[s= \frac{14 \pi}{9} \rightarrow s =\frac{14(3.14)}{9} \rightarrow s =\frac{43.96}{9}\] \[s=4.8844444444444444444444\] the 4 after the second 8 is repeating, so it's considered a repeating decimal.
JayDelV
  • JayDelV
Thank you !

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