Angle of view based on height and distance to a determined object

Question

I'm trying to determine what angle of view is needed for a photo shoot so that I can determine which super telephoto lens to rent.

I'm photographing an object thats 2,600 meters across from an altitude of 500 meters and a distance on the ground of 7,000 meters.

Thanks

Answer 1

distance $= \sqrt{500^2 + 7000^2} \approx 7018$

$2\tan \theta/2 = 2600/7018$ so $\tan \theta/2 \approx 0.185$, and $\theta/2 \approx 10.5$ degrees.

So your angle is about 21 degrees.