# Law of Cosines and Related Rates

1. Apr 19, 2006

### fstam2

Here is the question:
Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes?
I have:
dx/dt= 3 mi/h, dy/dt= 2 mi/h, dz/dt= ?
x= 3*.25= .75, y= 2*.25= .50
The instructor hint was to use the Law of Cosines:
$$z^2 = x^2 + y^2 - 2xy \cos \theta$$
My theta is 45 degrees.
My question is that I am plugging in values for all the variables, but I think this is the wrong direction.