A man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 14 ft high. At what rate is the length of his shadow changing when he is 60 ft away from the lamppost? g

Let be the distance between the lamppost and the man, and the length of the man's shadow cast by light. Then the man and lamppost form a set of similar right triangles (see image) in which

We can solve for :

Differentiating both sides with respect to time :

Since is changing at a rate of 7 ft/sec, it follows that is changing at a 25% slow rate, or 7*3/4 = 21/4 = 5.25 ft/sec.

47 - 90 = 43

43 - 180 = x

x = 137