You're saying you get two different distance readings and you want to calculate the position?
I think that's a Geometry problem. Draw a circle around each sensor, with the radius equal to the distance of the sensor's reading. There should be two points max where the circles intersect. The object should be in one of those two places.
I see you already found the solution in the pdf you linked.
Am I wrong in thinking this? However, it seems like this would only work IF the object was in-between both sensors.
There is no requirement for the object to be in-between both sensors. The equations will work even if the object is outside. And you don't really need to know the angles at all. The equations will give you x and y coordinates. If you arrange your point of view so that point A (Your left sensor) is the origin and point B (the right sensor) is along the X axis, the Y coordinate will tell you how far in front the object is, and the X coordinate will tell you how far to the left or the right it is.