Phones don’t just use triangulation. Modern smartphones will also use GPS (A-GPS).
In the US, E911 requires all phones to be able to report their physical location. Phone companies may use this ability to respond to police location requests. I don't know one way or another, but it seems likely.
The E911 laws, though, only require that the location information be obtained and forwarded when the call is placed.
So, I don't know. I don't know anything beyond that.