Tangent of what? Did you mean the tangent of the FOV angle?
Your formula (0.5*(plan width)/(camera distance)) is for the tangent of the half of the FOV angle.
0.5*(plan width)/(camera distance)
You can see more details on FOV zooming in the zoom section of my D3dScenePresenter - How to present and manipulate a 3D scene using MDX article.
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