Determining direction of polygons using QGIS?

Is it possible to get the direction of the longest side of a rectangle in QGIS?

I know how to get the direction of a line layer. But I need to know the direction of a polygon. One could start at the center of a polygon and find the shortest way to the border by using a line and take the direction of this line, but I don't know how to draw this line automatically for 30000 polygons.