kittycat1

Hi all,

can anyone help me.

I have a circle with a 3m radius.
The circle is split into 3 equal sctions all with 120 degree angles
so a-b is 3m b-c is 3m
what measurement is a-c?

Anyone as noone in my office can remember how to work this out.

Thanks guys

xxx

TheShed

Hmm, not sure what you are trying to solve? What do a, b, and c represent?

If you want the area of the circle, it is Pi x Radius (3m) squared = 88.82m

If you want the area of each segment if would be area/3 = 29.6m

Alternatively if you want the outer edge of each segment if would be 1/3 of the diameter which would be radius*3= 6 (Diameter) then Diameter* Pi = 18.84 m / 3 = 6.28m per segment

Hope it helps


try www.mathgoodies.com

kittycat1

ok its catwalk stage.

I need to know the length of the line between ac- so i know ab and bc are both 3 m- and the circle is split into 3 identical sections so must have 120 degree angle between ab and bc so i need the straight line length between a-c

TheShed

Can you describe what a,b,and c represent? Are they the points on the diameter where the three segments join each other or is one of the points the centre of the circle? If you want the curved line around a segment it is simply 1/3 of the diameter. If you want a straight line between two of the points it takes a bit more working out.

kittycat1

this might help so I need a-c length

kittycat1

I can honestly say I never thought I would use this information in real life! who knew eh!

jackthehat

5.196m Use the Sine or Cosine Rule (Phew that took me back!)

rossojo

http://en.wikipedia.org/wiki/Hypotenuse

paca

5.2m

edit: this was rounded up, not worked out

kittycat1

Thank you jack- just for my own sanity can you tell me how you worked that out xxx

paca

I drew it in CAD

edit... just redrew it to fix the error.... worked out perfectly to 5.196

TheShed

Gotcha. This is called the chord length. I hope I have remembered this correctly. it should be Radius * (sq root (2-Cos of segment angle).

Therefore Angle = 360/3 = 120 ; Cos 120 = -0.5

2-(-0.5) = 2.5

6 * 2.5 = 15m

If we consider that the curved diameter of the segment was 29m, this sounds about right to me.

I am sure there are some engineers on here who could check my calculus and if The Dean reads it and I have it wrong, my life will be hell !!!

Hope it helps.

TheShed

whoops, I am out by a factor of three. If someone took the trouble to draw it out - take their advice, not mine
Hope it helps.

kittycat1

Thanks everyone! really reallllllly appreciated!

Just Browsing

What your looking for is called a chord. Basic function is 2rsin(c/2)

So, in your case its about 5.196m if my dodgy maths skills hold true.