Finding the Sum of Perpendiculars in a 24-Sided Polygon Inscribed in a Circle

  • Thread starter armolinasf
  • Start date
  • Tags
    Sum
  • #1
armolinasf
196
0

Homework Statement



There is a regular 24 sided polygon inscribed in a circle. A diameter is drawn and perpendiculars are dropped from all the vertices on that side of the diameter. Find the sum of the lengths of the perpendiculars.

The Attempt at a Solution



I came across this problem and I have no clue how to approach it. I'm looking for a point in the right direction. Thanks for the help!
 

Attachments

  • get-attachment.jpg
    get-attachment.jpg
    15 KB · Views: 380
Physics news on Phys.org
  • #2
hi armolinasf!

well, what formula are you starting with? :smile:
 
  • #3
No formula was given. It was at the end of a section on trig identities, specifically using them to sum trig series.
 
  • #4
You have to find the formula. You have studied trigonometry haven't you?

ehild
 
  • #5
My first instinct was to write something like S=r+2(l1+l2+l3+l4+l5), where l is the length of each chord. Should I be looking for a way to express each l in terms of r?
 
  • #6
hi armolinasf! :smile:

yes, and the various angles (nπ/12)
 
  • #7
Yeah i finally realized that the height of each perpendicular is equal to the sine of the angles...So here my sum:

S=r+2r[sin(pi/12)+sin(pi/6)+sin(pi/4)+sin(pi/3)+sin(5pi/12)]
 
Last edited:
  • #8
Last edited by a moderator:
Back
Top