verticalangle

Vertical angle refers to the angle between the horizontal plane at the observer and the line of sight to a target, measured in the vertical plane that contains the line of sight. It is often called the elevation angle. Positive values indicate the target is above the horizon, while negative values indicate it is below.

In surveying and related fields, the vertical angle is related to other angular measures. The zenith angle Z is 90 degrees minus the vertical angle (Z = 90° − E). Elevation angles are typically recorded in degrees, minutes, and seconds, or in radians, using instruments such as a theodolite or a total station.

Measurement and calculations: If the line-of-sight distance to the target is L, the vertical angle E yields a height difference h = L sin(E) and a horizontal distance d = L cos(E). If the horizontal distance is known instead, the height difference is h = d tan(E). These relationships enable height and distance calculations in triangulation, construction, and navigation.

Applications: Vertical angles are used to determine elevations of features, to stake out construction points, and to measure altitude differences. In astronomy, elevation angles describe an object's position above the horizon.

Limitations and refinements: Precise work may require corrections for atmospheric refraction, instrument errors, and target misalignment. Modern instruments also account for systematic biases to improve accuracy.

See also: elevation angle, zenith angle, theodolite, total station, trigonometry.