If we place the origin of the coordinate system at the bridge level midpoint between the two towers, 
we have the vertex of the parabola at the point (0,10).


So, we write an equation of the parabola in vertex form

    y = ax^2 + 10.


Coefficient "a" is unknown.  It is the only unknown in this problem now.


To find it, we use the condition at the endpoint: y= 40 at x= 120/2 = 60.  It gives

    40 = a*60^2 + 10

    40 - 10 = a*3600

       30   = 3600a

        a   =  = .


Thus the parabola is  y = .    


Having this equation ready, we substitute x = 50 ft into the equation 
and find the height of the cable at the point x= 50, which is 10 feet from the end of the bridge


    y =  = 30.833 ft   (rounded).    ANSWER