Basic Related Rates: Rate of change of length of shadow

[Michael_J]

Homework Statement

A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his shadow is increasing in length.

Homework Equations

Pythagorean Theorem, Theorem of Similar Triangles (ratios of corresponding sides are equal)

The Attempt at a Solution

I am not actually not sure about how to start here. What confuses me is the shadow length; we know that the rate of change (or derivative) of the man's distance away from the lamppost is 3ft/s, but I am not sure where to go from here.

Help would gladly be appreciated.

 

[dextercioby]

You're allowed to make the assumption that he starts off from the same place with the lamp, so that he's exactly 3ft away from it after 1 second.

 

[HallsofIvy]

Start by drawing a picture. Draw the ground as a horizontal line, the lamp post as a vertical line, the man as a second, shorter, vertical line. The line from the tip of the lamp post to the tip of the man's head touches the ground at the tip of the shadow. You will see two similar (right) triangles there. The smaller has the height of the man as one leg, the length of his shadow as the other. Corresponding sides on the larger triangle are the height of the lamp post and the sum of the length of the shadow and the man's distance from the lamp post.