Browning Hi-Power Magazine: Trigonometry

The Browning Hi-Power magazine case has a 12.5° forward angle with respect to the floor plates:

Browning Hi-Power magazine - components
Browning Hi-Power magazine – components

The natural axes lie parallel and perpendicular to the case axis, which means dimensions parallel and perpendicular to the floor plates (horizontal & vertical, respectively) require a bit of trigonometry. This doodle sketches some of the key values, not all of which are hereby asserted to be correct:

Magazine angle doodles
Magazine angle doodles

Name the variables:

  • Slant angle α
  • Height H along magazine axis
  • Length L perpendicular to H

Components of H:

  • vertical = H cos α
  • horizontal = H sin α

Components of L:

  • vertical = L sin α
  • horizontal = L cos α

Extreme point of the tilt at the edge, relative to center point on axis:

  • vertical = (L/2) sin α
  • horizontal= (L/2) cos α

Projection of top parallel to axis onto horizontal:

  • L / cos α

I suppose one could set up functions for all that, but I tend to just hammer out the trig where it’s needed.