Distance between two antennas I am trying to find out the formula to calculate how high antennas need to be for Line of Sight (LoS) propagation.
I found:
d = 3.57sqrt(h)

also
d = 3.57sqrt(Kh)

$d$ can also be worked out using
d = 3.57( sqrt(K[h1]) + sqrt(K[h2]) )

Where $d$ is the distance between an antenna and the horizon (or between two antennas) in kilometers, $h$ is the height of the antenna(s) in meters, and $K$ is used to account for the curvature of the earth (which is usually $\frac{4}{3}$).
The problem with this equation is it is making the antennas ridiculously high for the distance I am trying to calculate. The question I am trying to answer is: “Two antennae are used for line of sight propagation. The antennae are spaced $150$ km apart. Determine the required antennae heights.”
My calculations:
d=3.57sqrt(4/3)(h)
d=3.57(sqrt[4/3])(sqrt[h])
d=3.57(1.1547)(sqrt[h])
150=(4.1223)sqrt(h)
150/4.1223=sqrt(h)
sqr(36.3875)=sqr(sqrt(h))
1324.05=h   1324meters = h1 + h2  -> each antenna needs to be 762meters high

Is this the correct method? Or have I chose the wrong equation totally?
 A: The exact distance, $d$, from the top of the tower of height $h$ to the horizon is
$$
d=\sqrt{2rh+h^2}
$$
where $r$ is the radius of the Earth. However, if we assume the height of the tower is insignificant in comparison to the radius of the Earth, we can make the following distance approximation:
$$
d=\sqrt{2rh}
$$
Since $r=6371000\text{ m}$, This gives
$$
d=3570\sqrt{h}
$$
where $d$ and $h$ are measured in meters.

As I mentioned in a comment to Abel, if you have two towers of height $h_1$ and $h_2$, the maximum distance between them is the sum of each of their distances to the horizon; that is,
$$
d_1+d_2=\sqrt{2rh_1}+\sqrt{2rh_2}
$$
$\hspace{4.5cm}$
If the towers are of equal height $h$, then the maximum distance between them is $2\sqrt{2rh}$
$$
d=7139\sqrt{h}
$$
A: A:  the first formula is the correct one.  It is based on the curvature of a spherical earth.  The reason for the variable $K$ is unclear.
B:  Picture yourself seated at ground level, exactly between the two antennas (75 km from each)  Each antenna must be tall enough to just reach you at that antenna's horizon.  IOW, use 75 km for the distance in the first equation, to give the height of each antenna.
A: I thought I'd just show you where the right equation comes from.
Your situation is shown in the following picture. The earth is depicted green, the LOS is depicted red and the radius of the earth as well as the antennae are depicted black.

From this picture we see that Pythagoras' Theorem applies and we have $(R+h)^2=R^2+\left(\frac{d}{2}\right)^2$. Expanding $(R+h)^2$ now gives us $2Rh+h^2 = \left(\frac{d}{2}\right)^2$ and since $h<<R$ we may neglect the $h^2$ to obtain $2Rh = \left(\frac{d}{2}\right)^2$ and finally $$h = \frac{d^2}{8R}.$$
In your case this gives $h = \frac{\left(150\,\mathrm{km}\right)^2}{8\cdot 6378.1\,\mathrm{km}} \approx 441\,\mathrm{m}$.
