anonymous one year ago The arc length of the circle is 100 degrees and is 7 meters. Find the perimeter of the sector.

1. jdoe0001

hmmm the arc length is 100 degrees? as opposed to 100 meters?

2. anonymous

I have no clue. i guess its safe to assume that cause all it says is the arc length is a 100 degrees. The length of that stretched out is 7 meters. So i have to find the perimeter of the sector which i dont even know what that is.

3. jdoe0001

|dw:1441238511043:dw|

4. anonymous

|dw:1441237812416:dw|

5. anonymous

I thought that was the arc length

6. anonymous

cause thats the central angle

7. jdoe0001

right, but the arc's lenght is not given in degrees, it'd be a flat measuring unit, like meter, or feet now, the central angle of the arc, would be 100 degrees

8. anonymous

o

9. jdoe0001

so..hmm it sounds a lot like |dw:1441238753083:dw| if that's the case, all you'd need to get is the arc's length and sum it to the radii given

10. anonymous

Yeah... i dont really know how to do that

11. jdoe0001

$$\bf \textit{arc's length}=s=\cfrac{\theta\cdot \pi\cdot r }{180}\impliedby \theta\textit{ in degrees}$$

12. jdoe0001

so the perimeter is 7 + arc's length + 7

13. anonymous

Am i suppose to get a decimal??

14. jdoe0001

yes

15. anonymous

can i put 16pi/3 for exact???? as the arc length??

16. jdoe0001

well.. you could also keep as rational as well got any choices on what's expected? float or rational?

17. jdoe0001

sure

18. anonymous

so 30.7552????

19. jdoe0001
20. anonymous

hmmm

21. anonymous

what would be the exact form

22. jdoe0001

ohh .. one sec

23. jdoe0001

$$\bf \cfrac{\theta\pi r}{180}\implies \cfrac{100\cdot \pi \cdot 7}{180}\implies \cfrac{35\pi }{9} \\ \quad \\ 7+\cfrac{35\pi }{9}+7\implies 14+\cfrac{35\pi }{9}$$

24. anonymous

That would be the perimeter?

25. jdoe0001

yes

26. jdoe0001

we could use 3.1416 for $$\pi$$ , then again, that'd make it a float, or decimal :)

27. anonymous

yeah. Can u help me on one last question please??

28. anonymous

Solve using S=r(theta) Radius Central Angle Arc length ? pi/3 3/2 m

29. jdoe0001

very straighforward you said it ->S =r(theta)

30. jdoe0001

$$\frac{\pi }{3}$$ is already in radian units so S = r * $$\theta$$

31. anonymous

3/2 = r(pi/3)

32. anonymous

@jdoe0001

33. anonymous

@jim_thompson5910

34. anonymous

everytime i solve it i get a weird decimal and its confusing me