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Topic: Trying to find perimeter of a regular pentagon
Replies: 36   Last Post: May 31, 2013 9:26 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Trying to find perimeter of a regular pentagon
Posted: May 28, 2013 7:41 PM

On 29 Maj, 00:45, JT <jonas.thornv...@gmail.com> wrote:
> On 28 Maj, 23:24, Ken Pledger <ken.pled...@vuw.ac.nz> wrote:
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> >  130bcd <carl.sundqu...@gmail.com> wrote:
> > > .... I have unsuccessfully tried to find the perimeter of a pentagon. The "radius"
> > > to the vertices is 130, which I tried to convert into 5 triangles but I can't
> > > find a formula for determining the length of the 3rd side of an isosceles
> > > triangle.

>
> > > The two equal length sides would, of course be 130 and the angle between them
> > > would be 72....

>
> >    If a regular n-gon is inscribed in a circle of radiu r, then each
> > side of the n-gon has length  2r.sin(pi/n).  In your case that means
> > 260.sin(pi/5)  or  260.sin(36 degrees).

>
> >    That can actually be expressed in terms of square roots if you like,
> > since  sin(36 degrees) = (1/4)sqrt(10 - 2.sqrt(5)).  Such expressions
> > involving sqrt(5) underlie the construction of the regular pentagon by
> > straightedge and compasses (Euclid IV.11, or a neater construction by
> > Ptolemy).

>
> >       Ken Pledger.
>
> http://www.wolframalpha.com/input/?i=260+sin+%28pi%2F5%29++
> Is 152 correct for the side length?
>
> Maybe i am lost here but if the side is 130, we can divide the
> isoceles into two right angled triangles each with 31 degree angle
> correct?
> and the hypotenuse of each is 130 and the angle 31. I just plugget it
> in herehttp://www.cleavebooks.co.uk/scol/calrtri.htm
> And then i see that the height for each must be 67 * 2 = 134 * 5 what
> did i do wrong?

I know usally 72/2 = 36 ;D

Date Subject Author
5/28/13 130bcd
5/28/13 JT
5/28/13 JT
5/28/13 Barry Schwarz
5/28/13 JT
5/28/13 JT
5/28/13 JT
5/28/13 JT
5/28/13 Ken.Pledger@vuw.ac.nz
5/28/13 JT
5/28/13 Ken.Pledger@vuw.ac.nz
5/28/13 David Bernier
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/30/13 RGVickson@shaw.ca
5/31/13 Brian Q. Hutchings
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 Brian Q. Hutchings
5/28/13 JT
5/28/13 JT
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/29/13 Richard Tobin
5/29/13 JT
5/29/13 Richard Tobin
5/29/13 Brian Q. Hutchings
5/29/13 JT
5/29/13 Brian Q. Hutchings
5/30/13 Graham Cooper
5/30/13 RGVickson@shaw.ca