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Here's how I'd do it.
theta is the angle between the line from the top of the lamp post to the tip of the shadow.
x is the displacement of the man from the lamp post.
s is the displacement of the shadow from the lamp-post.
theta = tan^-1(9/x) (triangle (0,15),(x,6),(0,6))
tan(theta) = 15/s (triangle (0,15),(s,0),(0,0))
s = 15/tan(theta)
s(x) = 15x/9
dx/dt = 5
ds/dt = (15/9)(dx/dt)
=75/9
=8.33 ft/s
I think you got your similar triangles mixed up. But there you go.
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