I want to have one part of the text on the white triangle with it looking like it is disappearing behind the image behind the white triangle. How do I make the text appear on top of the white triangle and then behind the rest of the image at the same time? I am working in Illustrator. Image below.
Took me a while to understand your problem, but I think i've got it:
You have a white triangle on top of an image, or maybe the white triangle is part of the image? Anyway, you need to have your image contained inside a triangular shape. Construct the upper right triangle (the grey box symbolizes your image):
Now, select both the image and the triangle you just made, and choose
Object/Clipping Mask/Make. This will transform the triangle (the uppermost object) to a mask containing your image:
Now you can place text behind the grey triangle:
I suggest using the pen tool to draw the shape of the area where you want the text to appear, then use that as a clipping mask. This is the most straightforward and easy way to do what you want, I think.
If you aren't familiar with clipping masks, here's a tutorial you might find useful.