Question 16472
Very interesting problem.  I think I might be able to help with this one.  I'm sure you have it drawn up with the cord of 30" and a radius at the end of each cord.  The radius is the unknown, say x, for this problem.  Now, in addition to drawing the radius of x from the center of the circle to each endpoint of the cord, draw another radius right up the middle that will be perpendicular to the cord.  That will also be of length x, and it should illustrate the height that you want of 2.5 inches.  This radius up the middle also gives you two right triangles, that will allow you to use the Theorem of Pythagoras to solve.  In each of these right triangles, the hypotenuse is the radius which is x, and one of the legs will be half of the length of the cord, which is 15.  The other leg of the triangle is just below the 2.5 inch height, and it's distance from the center of the circle is the length of the radius x minus the 2.5.  


So, do you see the right triangle and what the three sides are?  The legs are (x-2.5) and 15, and the hypotenuse is x.


Theorem of Pythagoras:  {{{ a^2 + b^2= c^2}}} so
{{{ (x-2.5)^2 + 15^2 = x^2}}}
{{{ x^2 - 5x + 6.25 + 225 = x^2}}}


Subtract x^2 from each side and combine the numbers together:
{{{-5x + 231.25 = 0}}}
{{{231.25 = 5x}}}
{{{x= 231.25/5 = 46.25}}} inches


I hope this is correct!!  Does it look right?  You should probably try this out to see if it really works before you make anything expensive with it.  It's a great application to answer the question we hear so often, "What good is math???"


R^2 at SCC