How fast is the angle changing right ...

NOW?!

A man 20 feet east of a spotlight walks north at a speed of 4 feet per second. The spotlight follows the man. 

How fast is the angle of the spotlight changing when the man has walked 16 feet?

t = 5.1 (slider from 0 to 7, step 0.05)
A: (20, t * 4)
B = Intersect(xAxis, yAxis)
C = Point(xAxis)
α = Angle(C, B, A)
D: (19, 4 * t)
E: (21, 4 * t)
F: (20, 4 * t + 2.5)
J: (21, 4 * t + 1.25)
c = Ellipse(A, F, J)
d, e = Tangent(B, c)
G = Intersect(c, e, 1)
H = Intersect(c, d, 1)
I = Point(c)
poly1, b, g, i, j, h = Polygon(B, G, I, J, H)
a = Segment(B, G)
f = Segment(B, H)
k = Segment(A, C)