At what distance from a VOR will two converging aircraft lose separation if their angle of divergence is 15 degrees?

To determine the distance at which two converging aircraft lose separation when their angle of divergence is 15 degrees, we use the concept of the effective width of the separation corridor established by their flight paths.

The separation between aircraft is typically maintained by ensuring that they are at least five nautical miles apart horizontally. When aircraft are approaching each other at a specific angle, the distance at which they will lose this required separation is related to that angle.

Using basic trigonometric principles, the formula to find the distance at which two aircraft will converge based on their angle of divergence is derived from dividing the required horizontal separation (5 miles) by the sine of half the divergence angle. For an angle of 15 degrees, we consider half of that angle, which is 7.5 degrees.

Calculating this gives:

1. Determine the sine of half the divergence angle:

sin(7.5 degrees) is approximately 0.1305.

2. Calculate the distance:

Required distance = 5 miles / sin(7.5 degrees).

This results in approximately 38.33 miles.

According to the question, we want to find the approximate distance in a manageable range. Among the provided options, 17 miles is the closest