## anonymous one year ago A regular n-gon is inscribed in the unit circle. What is the perimeter for each n below? a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?

1. anonymous

Aye, mate. I may be of some assistance. But first, I need a favor from ye. Tell me when the observatory is.

2. anonymous

What observatory?

3. anonymous

I really need help on this

4. geerky42

Do you know Trigonometry? Or at least Law of Cosines?

5. geerky42

If so, this site may helps: http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/lindsay2.html

6. anonymous

I've been on that website. I just don't get it. Can you please just solve for A and show the steps so I could do the rest? Thanks.

7. anonymous

I do know trig and law of cosines and sines

8. geerky42

What A?

9. anonymous

a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?

10. anonymous

Please show me how to answer some of them with the steps. Thank You.

11. anonymous

By A i meant n=3

12. geerky42

From site, our equation would be $$P = nc = n\sqrt{2-2\cos\left(\dfrac{360^\text o}{n}\right)}$$

13. geerky42

Do you understand how this equation was derived?

14. anonymous

P is perimeter, n is the n-gon, what is c?

15. geerky42

c is side.

16. anonymous

How do I find the side? I am only given the n.

17. geerky42

You can use law of cosines to find the length of sides:|dw:1436579931950:dw|

18. geerky42

n-gon is inscribed in unit circle, which has radius of 1.

19. anonymous

So lets try to solve a.) n=3. I will plug in n into 360/n so it will equal 120 degrees. Then I have no idea lol.

20. geerky42

Yes, Plugging in n=3, you would have $$P = 3\sqrt{2-2\cos\left(120^\text o\right)}$$

21. geerky42

You can just use calculator.

22. anonymous

p=5.2?

23. geerky42

Yeah I got approximately that.

24. anonymous

So first I divide 360 by n, and then plug it into the formula?

25. geerky42

Actually, you just plug in whether value of n, then calculate.

26. geerky42

For case of n=3, you just plug in n=3 and calculate $$P = 3\sqrt{2-2\cos\left(\dfrac{360^\text o}{3}\right)}$$

27. anonymous

Oh I see. Thank you. What about if n = 542?

28. geerky42

Same. Plug in n=542 then calculate $$P = \textbf{542}\sqrt{2-2\cos\left(\dfrac{360^\text o}{\textbf{542}}\right)}$$

29. anonymous

Great, thanks. And lastly could you please explain part h.

30. anonymous

h. The perimeter in part f should be close to what number? How close is it?

31. geerky42

Well, imagine if n goes to infinity, what would n-gon become into?

32. anonymous

a circle

33. geerky42

Right. Saying we have case of $$n=\infty$$. How can we find perimeter?

34. geerky42

Or should I say "circumference"?

35. anonymous

$\pi radius squared$

36. anonymous

37. geerky42

That's area of circle. We want circumference.

38. anonymous

2pi*r

39. anonymous

40. geerky42

Yeah. Here, we have UNIT circle, so radius is 1. So part f should be close to $$2\pi$$

41. anonymous

42. geerky42

Yeah. Though I am not sure how to answer "How close is it?" I guess subtract part f from $$2\pi$$.

43. geerky42

But I think you did your job good enough lol...

44. anonymous

Thank you. This helped me so much.