Originally Posted by copaco
page 84.The Practical Pilot Leonard Eyges.D=60H/A°.How can that be?H is height of lighhouse on chart.
The triangle can be described in terms of H, α and Distance:
Distance = H / tan(α)
where, the angle is in radians (0—2π) and both height and distance are in metres.
The relations between radians and degrees is:
α = A * π / 180
with “A” being the same angle in degrees.
To describe angle A in minutes total, then A * 60 = a, thus α = (a / 60) * (π / 180). So, α = a / 3438, “a” being the angle in arc
Fact: tan(x) = x, if angle x is small.
Resulting in (with π = 3.14): Distance (m)= H * 3438 / a
Furthermore, distance in Nautical Miles = distance in meters / 1852.
Voilà, a very practical equation:
Distance = 1.856 * H / a
It contains just two approximations, both of neglitible influence. First, we left out the tan function and second we used 3.14 for π.