– Xochielt Sanchez
Answer by Robert Frost:
So, here's a diagram representing the scenario in the question. We can see our two ellipses, the Sun, Venus, and Earth. We can also see the day/night sides of the two planets.
Now, imagine we are standing near that day/night terminator (we're at the red x in this next picture). Our horizon (the line that separates the sky we can see from the sky we can't see) is the new yellow line.
The Sun is below the horizon, so it is night for us. Venus is still above the horizon, but close to it. We can also see that our line-of-sight to Venus allows us to see part of its day side and part of its night side. This last picture represents our actual perspective from the location of the red x.
We can't see the Sun, because it has set below the horizon. There is still a glimmer of light on the horizon, from the sun. And there, just above that glimmer of light, where the sky is starting to get really dark , we can see Venus.
Because the Earth is rotating at 15 degrees per hour, Venus will not be visible for long. Depending on the latitude of the observer, Venus can be up to around 30 degrees above the horizon, giving up to two hours of visibility.