If a bird fly to height of $h$ ,What's the area that it can see? Suppose a bird fly to height $h$ from earth . The bird can see area under by it's eyes ,name as $S$ ,What's $max \{S\}$ ?
Is it possible to solve  ?
my first trial was to assume a cone by $height =h$ and $S=\pi R^2$ as area like the figure I attached with.
Is $S$ a constant for special amount of $h$ ?
can we calculate $max \{S\}$ or $S$?(or something is missed  ?)
Thanks for any hint ,in advance.

I am assuming that there is no limitation on the angle of vision of the bird.
The only known values I am assuming is the half apex angle $\theta$.
By property of tangent, the half angle subtended at the center will be $90-\theta$.
By using the solid angle formula,
$$
A=\phi r^2=2\pi(1-\cos{(90-\theta}) = 2\pi (1-\sin{\theta})
$$
