A Total Station is a surveying instrument that combines an electronic theodolite (for measuring horizontal and vertical angles) and an Electronic Distance Measurement (EDM) device. It measures angles and distances and converts them into coordinates using geometric equations. 1. Conversion from Polar to Cartesian Coordinates (XYZ) When the instrument measures: Horizontal angle (θ), Vertical angle or elevation angle (α), Slope distance (S), It calculates the coordinates of the unknown point using the following equations: X = X₀ + S × cos(α) × sin(θ) Y = Y₀ + S × cos(α) × cos(θ) Z = Z₀ + S × sin(α) Where: (X₀, Y₀, Z₀) are the coordinates of the instrument (station), θ is the horizontal angle (from a reference direction), α is the vertical angle (from the horizontal plane), S is the slope distance to the point. 2. Horizontal Distance and Vertical Difference Horizontal distance (H) = S × cos(α) Vertical difference (ΔZ) = S × sin(α) 3. Angle Calculation Using the Cosine Rule To find angles in a triangle between three points: cos(θ) = (a² + b² - c²) / (2ab) 4. 3D Distance Between Two Points To calculate the spatial distance between two points: D = √[(X₂ - X₁)² + (Y₂ - Y₁)² + (Z₂ - Z₁)²]