A star-gazing robot spots Betelgeuse at 14 degrees above horizontal, Polaris at 16 degrees above that, and Alpha Centauri at 20 degrees above Polaris. If these three stars are collinear, and if the line connecting them is perpendicular to the line of sight between the robot and Alpha Centauri (which is 4.40 light-years away from Earth), then what would be the total distance of a trip from Earth to Betelgeuse to Polaris, back to Earth, and finally to Alpha Centauri? (Ignore relativistic effects and the curvature of space.)

And the answer is ...