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anonymous
 one year ago
Can someone please help me?
A regular ngon 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
The perimeter in part f should be close to what number? How close is it?
anonymous
 one year ago
Can someone please help me? A regular ngon 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 The perimeter in part f should be close to what number? How close is it?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, there is no picture @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but, how do I find the side lengths?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, how would I do that for a 5gon inscribed in the circle?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2are u saying theyre both 60 or together they are 60?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is there some sort of formula to solve this? because to find the perimeter of a 542gon inscribed in the circle, using a formula to figure it out is what makes sense

dan815
 one year ago
Best ResponseYou've already chosen the best response.2do u want me to solve mahimas question or yours jhanny

dan815
 one year ago
Best ResponseYou've already chosen the best response.2mahmia this is what u do okay first see the length of one of the sides of tthis n gon and multibly by n

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, i don't understand. What do you mean by "see the length of one of the sides"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and do you mean multiply the length of the side by n?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Sorry, forget my explanation. I was missing some key concepts in it.

dan815
 one year ago
Best ResponseYou've already chosen the best response.2see the vectors from the center have 360/3 separation for 3 god 360/4 for 4 gon 360/5 for 5 gon and so on

dan815
 one year ago
Best ResponseYou've already chosen the best response.2now u can use the cos law to find the length of each side

dan815
 one year ago
Best ResponseYou've already chosen the best response.2or write a vector subtraction magnitude equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0could help me solve one of them so that i completely understand?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would i use the law of cos to find the length of each side?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2that is the length of each side so the periment is n*L

dan815
 one year ago
Best ResponseYou've already chosen the best response.2where L is a function of n defined up there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439175975995:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.2that formujla was from cos law

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@surjithayer would use that equation for all of the ngons?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3But dan, what is the actual formula?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@surjithayer would i substitutes the number of sides for n in that equation?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Well, you could also use \(P(n) = 2rn\sin\left(\frac{180}{n}\right)\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Where r is the radius of the circle and n is the number of sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how did you come up with that formula? @Jhannybean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, that makes sense @dan815

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3So if we have a pentagon, right, let's draw that out. dw:1438994108310:dw

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Now we know that each of these triangles would be an isosceles triangle, where 2 sides of the triangle are considered the `radii` of the circle, whereas the opposite side touching the circle is what we have to find. So now, \(a=b=\text{radius (r)}\) Therefore, we can apply the law of cosines. \(c^2=a^2+b^22ab\cos(C)\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3And just like @dan815 demonstrated, but with \(l=c\) \(c^2=r^2+r^22r^2\cos(C)\) Now we're missing one thing, and that is \(\angle C\) \(\angle C = \dfrac{360^\circ}{n}\)  replace this back in formula, and you get \(c^2 = r^2+r^2 2r^2\cos\left(\dfrac{360^\circ}{n}\right)\) That will give give you the side length of the pentagon, c dw:1438994818712:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but since the radius is 1, when you substitute it into the formula wouldn't you get 0 times the cos of 360/n? making the answer 0, which wouldn't make sense

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Solving for c, we have: \[c= \sqrt{2r^22r^2\cos\left(\frac{360^\circ}{n}\right)}\iff c=r\sqrt{22\cos\left(\frac{360^\circ}{n}\right)}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3No, when r=1 you do not get 0.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, order of operations, that's right i forgot

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3And lastly, all we have to do is multiply by the number of sides \[P= n\cdot c ~~\sf\text{where} ~ c=r\sqrt{22\cos\left(\frac{360^\circ}{n}\right)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, thank you so much for your help, that makes so much sense

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Great :D Glad i could help!
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