 Gravitational height and distance along a body axis

In uniform gravity a body's gravitational potential energy is its mass times gravitational acceleration times the Cartesian height of its centre of mass. If that height is represented by an axis distance $h$ and tilt angle $\theta$, it is $h\cos \theta$ and the energy becomes $Mgh\cos \theta$. Treating $h$ simultaneously as a Cartesian height would introduce an extra, unjustified cosine.