Inversely linear is a good approximation.
Imagine a 1,7m tall girl at 1 m distance b. Her head is at point B.
How does the size/length of an object vary with distance?
Let the girl walk away from you. Her size a stays the same. She appears smaller, because she is appearing under a smaller angle. Her angular size changes. Try to imagine it with the picture attached.
Using arctangent to calculate her angular size is the correct way. For small angles you can simplify:
Angular size is inversely proportional to its object distance, without using optical devices.
An object on full-field with focal length of 12 mm would be measured incorrectly. An error 2-5% in length measurement may be made. For fish-eye lenses this may be even worse. Hands-on rule: Use the inverse relationship if angular size is smaller than 10°.