What technique can be used to estimate the horizontal distance between an airplane and a reference point below the horizon? A technique that can b...

What technique can be used to estimate the horizontal distance between an airplane and a reference point below the horizon?

A technique that can be used to estimate the horizontal distance between an airplane and a reference point below the horizon is to use the fact that if a reference point is 45 degrees below the horizon, the horizontal distance from the airplane to the reference point is equal to the altitude.
For other angles, the approximate values indicated in the table and in Figure 7.10 can be used (the exact values are obtained from the distance = altitude/tan(angle) relationship).
The mathematical relationship is as follows: for small angles measured in radians, we have sin(angle) ≈ tan(angle) ≈ angle. Then we have angle ≈ XTE/distance, where XTE is the cross-track error.
With the knowledge of the cross-track error, a correction can be applied to return to the route. There are two cases: if the distance traveled corresponds to less than half the total distance, a correction that corresponds to twice the cross-track error in the opposite direction can be applied (method of the isosceles triangle). If the distance already traveled is greater than half the total distance, another method must be applied.