Calculate Camera tilt angle

Question

I have a camera I'd like to mount on a tripod. I know the FOV dimensions of the camera (22.5 deg V 31 deg H). I'd like to know at what height and what tilt angle to place the camera to be able to capture the two points of interest on the ground. Please see the figure below.

I have attempted a solution using basic trig but am not sure it is correct. Please help!

Answer 1

Your calculations are correct in my view.

If you have to include both the red points, you need to place your camera at an angle such that it encloses both the red points.

So, tan θ = d/h_c => θ = tan ^-1 d/h_c.

But, as you need to enclose both the points, your angle should be slightly greater than θ ( my suggestion --- some θ+ε, where 0.25 < ε < 1 ) to perfectly capture those 2 red dots.