Shadow Problems (No Calculator)

Question

A 6 ft tall man walks toward a 30 ft tall streetlight at a rate of 2 ft/sec . What is the rate of change for the length of the man’s shadow when he is 5 ft from the light?

Answer 1

Using similar triangles, the length of the shadow is always one fourth the distance between the man and the lamp (see video). So the rate of change of the length of the shadow is always -1/2.