Use the formula 


S =    (1)


for the arc length S, where "r" is the circle radius and  is the central angle in radians.


To use it, you need first to convert 128 degs 18 minutes to radians.


128 degs 18 minutes = 128*60 + 18 minutes = 7698 minutes.


 radians = 360 degs = 360*60 = 21600 minutes.


So, 128 degs and 18 nimutes =  = 2.2381 radians.


So, your equation (1) now becomes

36.90 = 2.2381*r.


From it,  calculate r = .


Then double your "r" to get he diameter.