A runner sprints around a circular track of radius 100 m at a constant speed of 7 m/s. The runner's friend is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200 m.

I attached a sketch of the problem so you can visualize what I'm doing.

I decided to use the law of cosines, is the distance between them:

Differentiating with respect to

When the

So no I plug everything into the equation for the time derivative of s:

This is very close to the answer in my book which is

I can't seem to find where I want wrong.