I'm making pocket holes to connect wood together with a jig, the Kreg 720. The 720 works by moving at an angle (which I'm trying to measure) to ensure the hole is drilled higher on thicker pieces.

The jig makes a hole like this at a 15 degree angle.

The 720 works like this:

I'm trying to calculate the length of the drill bit which I can set with a stop. The 720 has stops included for common wood, but I like to be exact and I need to understand the geometry of how the 720 works. I zeroed out an angle meter and found that the case is exactly 57 degrees.

But! I wanted to make sure that the drilling jig block moved at 57 degrees, so I used my caliper to measure the board thickness block at the bottom and the top. That gave me these measurements.

Per this geometry:

So $\theta = 45 \deg$ which is intuitive for a jig like this. However, the case seems mounted to match the $57 \deg $ that I measured. I also measured the picture in photoshop and got the $57 \deg $ as well.

I'm confused with how these could be different. Obviously the case doesn't have to match the internals, but $12 \deg$ is a big difference. I'm curious if anyone has looked at this.

$d$ is the measurement from the base to the bottom of the moving block. $s$ is the distance between the back base and the front of the moving block. (I would love better language for these pieces too!)

At the bottom: