When you say "one is the background", are you talking about a CSS background-image or are you referring to a foreground image that is in back of the arrow?
How much area is covered by the "background" image? Does it cover the full page or is it within a container somewhere on the page?... do you have several of these images and you want an arrow in the bottom right corner of each one?
What determines the height of the "background" image on the page? Foreground images are relatively easy; background-images have no substance... they are like a background-color. We need to know how the size of that image's container needs to be defined.
In other words, we need more information to understand what you want.
The picture is good, but it doesn't include the edges of the browser so we can't tell how much of the page it fills.
Code would help a lot.