Question 16472
HI Wyatt, here's a formula that could help solve your problem.  If you're interested, it came out of a math tables book (CRC Standard Mathematical Tables) which I have used since the early fifties in college.

{{{C = sqrt(4h(2R - h))}}}

Since you know C (the chord length) and h (the length of that part of the radius between the chord and the circumference), you can, with a little algebraic manipulation, solve for R, the radius.

{{{C = sqrt(4h(2R - h))}}}  Square both sides.
{{{C^2 = 4h(2R - h)}}} Divide both sides by 4h.
{{{C^2/4h = 2R - h}}} Add h to both sides.
{{{(C^2/4h) + h = 2R}}} Finally, divide both sides by 2.
{{{((C^2/4h) + h)/2 = R}}} This can be simplified a bit.
{{{R = (C^2 + 4h^2)/8h}}}

Now let's plug in your values of C (30") and h (2.5") and grind away.

{{{R = (30^2 + 4(2.5)^2)/8(2.5)}}}
{{{R = (900 + 4(6.25))/20}}}
{{{R = (925)/20}}}
{{{R = 46.25}}} inches.