We don't usually measure the anterior chamber depth per say. We usually just comment if the A/C is deep or shallow. And honestly this just comes from looking at tons of patients everyday.
Also if you want to know if a patient has narrow angles (at risk for angle closure glaucoma) the classic teaching is that you direct the beam at an angle of 60 degress at the limbus. If the distance from the peripheral iris to the posterior cornea is less than 1/4 the thickness of the entire cornea than the angle is narrow.
The depth of the anterior chamber is really only an issue in cases of hypotony causing a very shallow a/c. And you really only see these after glaucoma filtering procedures.
Personally when I get called from the ED anterior chamber depth is not something I'm really gonna expect you to tell me. Really all I want to know is a good history, visual acuity, pupils, motility, IOP, and what the eye looks like on slit lamp/penlight exam (i.e cornea clear, a/c clear, injected conj. etc). Usually with this information I can get a pretty good idea of what's going on.
Hope that helped.