The Mapping and Distance Tools website lets you determine the compass bearing between sets of points. Zoom in to your desired area, click on “Start A Course”, and then click on the points you want (or enter a name or address to create a point). The tool will put X’s on the points, drawing lines between them:
As you create each point, the location of each point, the distance to preceding and succeeding points, and bearing will show up in a table:
You can also draw a circle on the map, though the utility of that option escapes me. And if you want to see how it’s done, the source code is available.