Does an object spanning percentage of the Camera's FoV correlate with the object's image percentage? I am working on a virtual camera inside a game engine, which provides me with an FoV control, but no Focal length control (and no filming sensor dimensions short of aspect ratio), and I am less than a beginner in photography.
Now when I position the Camera in a specific location in the world, and I position an object in front of the camera such that the object covers 50 degrees of the camera field horizontally. The camera FoV is 100 degrees horizontally.[see image please].

Then I measure the object in the image and I find it covering around 40% of the image width instead of 50%.
What is the most expected mistake that I am making here?
Relevant information: I don't know the position of the virtual camera is the position in the middle of the lens itself, the position of the sensory retina, or the position in between.
@ Physician --- We can use trigonometry and set-up a condition whereby the horizontal angle of view will be 100°
On a full frame 35mm camera format demotions 24mm by 36mm, mount a 15mm lens and horizontal angle of view will be 100°
On an APS-C compact, the frame size is 16mm by 24mm. Mount a 10mm lens and the horizontal angle of view is 100°
In other words, the angle of view of camera system intertwines focal length and format dimension.
For the full frame camera above:
The image plane falls 15mm downstream from the lens.  The Image triangle has a height of 15mm. The size of the angle at the apex of this triangle is 50°. We bisect this triangle creating two right triangles. The angle at the apex is 25°. The height of this triangle is 15mm. If you draw this triangle, the height is the adjacent side and the base is the opposite size. The tan of 25° = 0.4663. Thus Opposite / Adjacent = 0.4663. Thus Opposite side = 15mm X 0.4663 = 6.9946mm. The length of the image of the object will be 2X this value = 14mm.
For the APS-C format:  The image plane falls 10mm downstream. Such as lash-up delivers a 100° horizontal angle of view. The image triangle angles are the same as for the full frame. Bisecting the image triangle, we get two right triangles each with a 25° apex. The tan of this angle = 0.4663. The height of this triangle is the focal length of the lens = 10mm. 10mm X 0.4663 = 4.66mm X 2 = 9.33mm. The image of the object will be 9.33mm long.