Moving Shadow

Question

A man 6 ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above th ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?

Answer 1

in 2 seconds the shadow goes from 6 to 0 feet

that's -3 ft/sec average change

2 secons earlier he was 20 ft away with a shadow of 12 feet

in 2 seconds the shadow went from 12 to 6 ft

that's -6 ft in 2 seconds

or -3 ft/sec

change in the shadow = -3 ft/sec when 10 ft away

construct some tight triangles to see this more clearly