What is the mathematical relationship between slant range, height, and planar range?

The correct relationship involves the precise application of the Pythagorean theorem, which describes the relationship between the three dimensions in a right triangle. In this context, slant range refers to the direct distance from an observer to an object, height is the vertical distance from the object to the observer, and planar range represents the horizontal distance from the observer directly beneath the object horizontally to the point directly below it.

According to the Pythagorean theorem, for a right triangle where the slant range is the hypotenuse and the height and planar range are the two other sides, the relationship can be expressed as follows:

slant range^2 = height^2 + planar range^2.

This relationship confirms that the slant range is indeed the longest side (the hypotenuse), while height and planar range are the two shorter sides of the right triangle formed by these distances. Understanding this geometric interpretation is crucial in aeronautical calculations, especially for pilots and navigators when determining the position of an aircraft in relation to different altitudes and distances.

The other choices incorrectly misrepresent the relationship, as they fail to adhere to the fundamental principles of right triangle geometry.