milky way - Is Zeta Reticuli within the Orion Arm?

Let's take a look!

While I can't quite track down the source of this image, I've found it throughout the web, so hopefully it's roughly accurate. I'm pulling it from the Wikipedia article on the Orion Arm.

In this image you can also see the Orion Nebula sitting (relatively) cozily to the Sun. The distance between the two is believed to be around 1350 light years. Zeta Reticuli, on the other hand, is believed to be a mere 39 light years from Earth. Given the orientation of these two locations and the relative distances, it would be hard to place Zeta Reticuli anywhere but firmly within the Orion Arm.

Not exactly rock solid evidence, but sometimes some back of the envelope deduction will do.