a man of height 1.8m walks away from a 5 m lamppost at a speed of 1.2m/s. find the rate at which his shadow is increasing in length

Question

what type of equation do you use to figure this problem out? 

Answer 1

There are two similar triangles involved.

The man's distance is 1.2t from the lamp post. The length of his shadow is s(t).

The right triangle formed by the lamp post and (the distance of the man from the lamp post+his shadow length)

is similar to the right triangle formed by the man's height and the length of his shadow.

5/(1.2t+s(t))=1.8/s(t)5s(t)=1.8×1.2t+1.8s(t)

3.2s(t)=1.8×1.2t

s(t)=.675t

ds(t)/dt=.675 in this case meters per second