Problem source

For this question, you may use the following 
approximations, valid if $\theta $ is  small: \ 
$\sin\theta \approx \theta$ and $\cos\theta \approx 1-\theta^2/2\,$.
A satellite $X$ is directly above the point $Y$
on the Earth's surface and can just be seen 
(on the horizon) from
another point $Z$ on the Earth's surface.
The radius of the Earth  is $R$ and the height of
the satellite above the Earth is $h$.  
\begin{questionparts}
\item Find the distance $d$
of $Z$ from $Y$ along the Earth's surface.
\item If the satellite is in low orbit (so that $h$ is
small compared with $R$),
 show that
$$d \approx  k(Rh)^{1/2},$$ where $k$ is to be found.
\item If the satellite is very distant from the Earth (so that $R$ is small
compared with $h$), show that 
$$d\approx aR+b(R^2/h),$$
where $a$ and $b$ are to be found.
\end{questionparts}