## JayDelV one year ago 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.

1. arindameducationusc

theta=L/R

2. UsukiDoll

hmmm my textbook is like this though for arc length $s = \theta r$

3. arindameducationusc

where L = arc legth and r radius... Now I hope you can solve it.... if not, ask me

4. UsukiDoll

s - arc length theta - the angle r - radius

5. UsukiDoll

I think we need to convert 40 degrees to radians $40 \times \frac{\pi}{180} \rightarrow \frac{40 \pi}{180}$

6. UsukiDoll

simplify that fraction first ^_^

7. arindameducationusc

Awesome @UsukiDoll Good job.. @JayDelV just follow @UsukiDoll

8. UsukiDoll

or we can reduce later.... $s = \theta r \rightarrow s = \frac{40 \pi}{180} \times 7$

9. JayDelV

I'm actually confused, sorry was eating.

10. 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

11. UsukiDoll

you were given an angle in degree mode. We can't use degree mode for this formula, so conversion to radians is necessary

12. UsukiDoll

it's best to reduce that fraction first.. otherwise you will be stuck with an even bigger fraction to reduce.

13. 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.

14. UsukiDoll

what is 280 divided by 10 what is 180 divided by 10

15. JayDelV

28 and 18

16. 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

17. JayDelV

14 and 9

18. UsukiDoll

yes so we have $s= \frac{14 \pi}{9}$ we can't reduce anymore, so we got our arc length ;)

19. JayDelV

Thank you so much for your time I really appreciate it!

20. JayDelV

Oh wait, the answers are in decimals.

21. UsukiDoll

ah no problem we can convert to decimals XD

22. 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.

23. JayDelV

Thank you !