I'm developing a game through BabylonJS and there's four values that are of interest. The environment around the person is a sphere. This sphere has radius 100. The person may move forward from the origin to stand closer to the wall of the sphere and they can theoretically change their field of view (in radians) in addition to going closer to the camera. I want to know what is the viewing angle if we were to look at this from the origin.
Each time I try to tackle this with trigonometry that I've learned thus far, I get more unknowns than I want. I would really appreciate any help.
edit: we also know that the person's new distance from the wall of the sphere is 20 times its viewing angle in radians. I.e. if the person is 20units away from the side of the sphere, it's viewing angle is 1Radian.
See the figure below. The main circle is radius $100$. The distance from the wall is $h$, which gives the angles $h/40$ and $\pi-h/40$. Then by the law of cosines we can write $$100^2=(100-h)^2+f^2-2(100-h)f\cos(\pi-h/40)$$, solve that for $f$ and use the law of sines to write $$\frac f{\sin BAD}=\frac {100}{\sin (\pi-h/40)}$$