It's an object method, not a standalone function, so it would look
like this (assuming start and end are Location objects):

float res = start.distanceTo(end);

As for an example of using SensorManager and SensorListener, I don't
have anything handy, but there is an example in the API demos:
http://developer.android.com/guide/samples/ApiDemos/src/com/example/android/apis/os/Sensors.html

If you're looking for a compass display, a good example of that is in
the Professional Android Application Development book from Wrox.  It
has both simple and complex compass examples to get ideas from.  I
don't think Android has any stock widgets for that kind of thing.

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