What is the maximum distance in nautical miles that can be represented by an altitude of 60° above the horizon?

To determine the maximum distance in nautical miles that can be represented by an altitude of 60° above the horizon, it's important to understand the relationship between altitude angles and distance.

When an object is observed at an angle of 60° above the horizon, it forms a specific geometric relationship in terms of distance. The maximum range of sight from that altitude can be calculated using the formula that relates the radius of the Earth to the distance to the horizon based on the altitude angle.

The maximum distance visible on the Earth's surface from a height can be approximated using the formula:

[ D = 1.414 \times h ]

where ( D ) is the distance in nautical miles and ( h ) is the height in feet.

For an observer at sea level looking at a point 60° above, the corresponding distance can also be analyzed through trigonometric principles; specifically, one can envision a right-angled triangle where the observer's height determines how far they can "see" before the Earth's curvature becomes a factor. The relationship indicates that as the angle of elevation increases, the potential distance seen increases dramatically.

At an altitude of 60°, the maximum distance correlates to approximately 1800 nautical miles, which reflects the Earth's