For simplicity, let assume that the origin of the coordinate system is placed on the ground EXACTLY at the symmetry line of the parabola.


Then the equation of the parabola in this coordinate system is 

y = a*(x+40)*(x-40) =  = ,

where 40 is half the distance between the arc's foots, and "a" is some unknown coefficient.


You need to choose the value of "a" in a way to provide its arc height 200 ft at x = 0. So, your equation for "a" is

200 =  = -a*1600,

which gives you  a =  = .


Thus your parabola is  y = .     (1)


Now to find the height at x = 20 ft, you need simply substitute x= 20 into the formula (1).  You will get


    The height of the arc at x= 20  is  y =  =  =  = 100 ft.


Answer.  The height of the arc at x= 20  is  100 ft.