Contradictions in dominant beliefs around Sirius, derived from R/tan θ = D

edit: should be in radians. so not much of a contradiction. My assumption is that Sirius is closer, I was thinking from that point of view. Another possibility there, is that the distance between "Sirius B" (which I think is an exoplanet) and Sirius is smaller. With 10 AU and trigonometry, the distance becomes around 3 light years.

The largest separation between Sirius and its exoplanet (by many believed to be another star, "Sirius B") is 11 arc seconds, and the distance between them is often estimated to be 20 AU. With that 20 AU estimate, to get the distance from our solar system to Sirius, we can model an object that is 20 AU in diameter, and that has an angular diameter of 11 arc seconds. We can then feed it into the formula R/tan θ = D, 20 AU/tan(11/3600) = 0.1 light years.