# Thread: The Spotlight: a related rates problem

1. ## The Spotlight: a related rates problem

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.9 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

As always, thanks in advance, you guys are awesome!

2. More similar triangles.

I will post a diagram here in a little bit.

Similar triangles:

$\frac{y}{12}=\frac{2}{12-x}$

$y=\frac{-24}{12-x}$

$\frac{dy}{dt}=\frac{24}{(x-12)^{2}}\frac{dx}{dt}$

dx/dt=-1.9 and x=4:

$\frac{dy}{dt}=\frac{24}{(12-4)^{2}}(-1.9)=\frac{-57}{80}\approx{-0.7125} \;\ m/sec$