Step 3: Calculations
First we need to figure out the displacement of the CPU fan when looking at it from above. In my example, the fan was 1-1/4" lower and 3/8" to the right of the vent hole. Plug this into the Pythagorean formula to get a displacement of 1.305" (about 1-5/16").
The number we just found is crucial for the next step. We need to figure out how long to cut the PVC and at what angle. We know the CPU fan sits 3-1/2" into the case, but we can subtract 1/4" because of the plywood piece that mounts the PVC. That leaves us with 3-1/4" deep and skewed 1-5/16" laterally. The Pythagorean formula gives us a total length of 3-1/2" for the PVC.
The angle can be figured out using tangent. With the opposite and adjacent sides known, one can easily figure out the angle theta in the third diagram. However, the saw must be set to cut at an angle of 22 degrees, not the 68 we found (90 - 68 = 22).