Given R = 5", F = 54", and r = 1.3 / 2 = 0.65: Using the formulas in the diagram gives angle c = 5.3128°, and a = 6.9898". These values remain constant throughout the rest of the calculations.
Now it is time to consider the upper triangle ABC.  The first thing to note is that angle B for this triangle is the sum of 90° and 45° = 135°. We can now find the remaining angle in the upper triangle by subtracting angles c and B from 180.  By the Law of Sines: side c = a sin c / sin A = 1.0135".  Likewise, in the lower triangle A'BC, the angle B is given as 45°.  Thus angle A' = 180° - 45° - 5.3128° = 129.6872°. Here side c' = a sin c / sin A' = 0.8410, and we can add side c to side c' to get our flat's new length of 1.8545".