Related Rates: Man and Spotlight

[Lancelot59]

1. The problem statement, all variables and given/known data
A 2m tall person walks toward toward a wall at 1.6 m/s. A spotlight 12 m away from the wall shines at it. How fast is the length of his shadow on the wall decreasing when he is 4m away from the wall?

I tried a few different things with trig, none of which worked.

[lanedance]

like what?

[Lancelot59]

Well, actually I couldn't figure out how to setup the equation to begin with.

[lanedance]

ok so start by drawing a picture, and try and relate the distnace of the man from the light or wall to the height of the shadow - think similar triangles

[Lancelot59]

Yeah, that's where I run into problems.

[lanedance]

ok so what do you need a hand with?

[Lancelot59]

How can I go about setting up the problem? How can I go about finding an equation to solve? I understand how to solve these problems, but not how to go about setting up their equations.

[erok81]

Think about the spot light creating a triangle and then insert the man to create a second smaller triangle. Using the numbers you have in the question, you can get your equation from that by setting the two similar triangles equal to each other - I can't remember the exact name for that, sorry. Ex. base/height of triangle one = base/height of triangle two then cross multiply and solve for your unknown that may or may not start with an s.

[Lancelot59]

I managed to get it. Sorry it took so long to get back. Thanks for your help!