Arctanheight

Arctanheight is a mathematical function that assigns to a pair of values—the vertical height h and the horizontal distance d—the elevation angle θ between the horizontal plane and the line of sight to a point at height h located at distance d from the observer. It is commonly defined by θ = arctan(h/d) when d ≠ 0. The domain includes all real heights and nonzero horizontal distances, and the typical range is (-π/2, π/2) in radians (or -90 to 90 degrees).

Variant forms extend the concept to handle all directional cases. Using the two-argument form atan2, arctanheight can be written as θ = atan2(h, d), which yields the correct angle for any sign combination of h and d and is robust when d is negative or zero. If one uses the simple arctan, special-case handling is required for d = 0 to avoid division by zero and to correctly reflect the quadrant.

Examples illustrate the idea. For h = 10 and d = 2, θ ≈ 1.3734 radians (about 78.7 degrees). For h = -5 and d = 3, θ ≈ -0.9828 radians (about -56.3 degrees).

Applications of arctanheight appear in areas such as surveying, camera and graphics engineering, robotics, and line-of-sight calculations, where elevation angle from a reference point to a target is needed. The concept is closely related to the standard arctan function and its two-argument variant atan2, which generalizes the calculation to account for sign and direction in a planar setup. See also arctan, atan2, elevation angle.