1. ## Simple Trig Problem.

I have a circle. 5 hole equally spaced. A line running from hole 1 to 3. Length of this line is 3.000 inches. What is the diameter of the cirlcle?

Any help would be appreciated.

I have a circle. 5 hole equally spaced. A line running from hole 1 to 3. Length of this line is 3.000 inches. What is the diameter of the cirlcle?

Any help would be appreciated.
Several things are unclear, including: How do the holes relate to the circle? How does the line run from hole 1 to hole 3? What do the holes look like?

Either explain the question more clearly or (and this is the prefered option) attach a diagram.

The word "holes" is confusing.
Did you mean "points"?

I have a circle with 5 points equally spaced.
A line running from point 1 to point 3 has length of 3.000 inches.
What is the diameter of the cirlcle?
Code:
      A
o *
|\    *
| \      *   B
r |  \       o
|   \
|    \ 3    *
|     \     *
O o 144° \    *
*    \
r  *  \ *
o
C

The circle has center $\displaystyle O.$
Point 1 is $\displaystyle A$, point 2 is $\displaystyle B$, point 3 is $\displaystyle C.$
Diagonal $\displaystyle AC = 3.000$ inches.
Note that: .$\displaystyle \angle AOC \,=\,144^o$
The radius is: .$\displaystyle r \:=\:OA \:=\:OC$

Law of Cosines: .$\displaystyle r^2 + r^2 - 2r^2\cos144^o \:=\:3^2$

. . $\displaystyle 2r^2 - 2r^2\cos144^o \:=\:9 \quad\Rightarrow\quad 2r^2(1 - \cos144^o) \:=\:9$

. . $\displaystyle 4r^2\left(\frac{1-\cos144^o}{2}\right) \:=\:0 \quad\Rightarrow\quad 4r^2\sin^272^o \:=\:9$

. . $\displaystyle r^2 \:=\:\frac{9}{4\sin^272^o} \quad\Rightarrow\quad r \:=\:\frac{3}{2\sin72^o} \:=\:1.577193336$

The diameter is: .$\displaystyle d \;=\;2r \;=\;3.154386673 \;\approx\;3.154\text{ inches}$

4. Thank you soroban. Yes I did mean points, the trade im studying for uses the term holes. But the proper term is points, and thank you your soloution is very helpful.