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Here it is without the trig:
Same variables:
x is the displacement of the man from the lamp post.
s is the displacement of the shadow from the lamp-post.
Using similar triangles:
6/(s-x) = 15/s
6s=15(s-x)
s=(15/9)x
ds/dx = 15/9
ds/dt = (ds/dx)(dx/dt)
ds/dt = (15/9)(5 ft/s)
ds/dt = 8.333 ft/s
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