Which of the following is not a side of the astronomical triangle?

The astronomical triangle is a concept used in spherical astronomy to relate celestial objects and their positions in the sky. It is typically defined by three key components: the zenith distance, the altitude, and the azimuth of an astronomical body.

The correct answer identifies the vertical angle as not being a side of the astronomical triangle. This is important because the vertical angle is more commonly used in a different context, particularly in surveying and measurement, rather than directly relating to the celestial positioning represented by the astronomical triangle. The sides of the astronomical triangle specifically involve terms that directly correspond to the celestial sphere or the coordinates used to locate stars and other celestial bodies.

Colatitude and polar distance are indeed sides of the astronomical triangle. Colatitude refers to the complement of latitude, which is vital in determining celestial coordinates. Polar distance is the angle from the pole to the point of interest in the celestial sphere, which is also integral to the triangle's geometry. Coaltitude, a less common term but related to altitude, signifies the same concept of measuring the height of an object above the horizon and can be associated with the astronomical triangle.

By understanding these components and their relevance to astronomical positions, it becomes clear why the vertical angle does not belong as a side of the