There are a couple of ways to work this problem. Perhaps the easiest is to make use of secant rules.
The product of the two halves of the chord will be the product of the height of the segment and the missing length of the rest of the diameter (x). Then we have
.. (1180/2)^2 = 225.4*x
.. x = 590^2/225.4 ≈ 1544.4
The diameter is 225.4 +1544.4 ≈ 1770 . . . . feet.
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Another way to solve it is to consider the right triangle formed by the radius and the chord. Let the radius be represented by r. Then the Pythagorean theorem tells you
.. r^2 = 590^2 + (r -225.4)^2
.. r^2 = 590^2 +r^2 -450.8r +225.4^2
.. 450.8r = 590^2 +225.4^2
.. r = 398,905.16/450.8
.. r ≈ 884.88
.. d = 2r ≈ 1770 . . . . feet
