A man 6ft tall walks at a rate of 6ft/s away from a lamppost that is 23 ft high. At what rate is the length of his shadow changing when he is 65 ft away from the lamppost?

Suppose,

x = distance of the man

s = length of the shadow

Using the idea of similar triangles

6/s = 23 / (x + s)

Simplifying:

we get,

6 (x + s) = 23s

6x + 6s = 23s

6x = 17s

Differentiating with respect to time,

6 (dx/dt) = 17 (ds/dt)

Manipulating the above equation for ds/dt,

ds/dt = (17/6) (dx/dt)

ds/dt = (17/6) (6)

ds/dt = 17 ft/sec.