Angle of Elevation

Author

Eric W. Weisstein
September 1, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Trigonometry/AngleofElevation.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/AngleofElevation.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

The angle from the observer's horizontal line upward to the line of sight.

Module[{angleColor,observer,point,theta,ink},observer={0,0};point={(16/5),(7/5)};theta=ArcTan[(7/16)];angleColor=RGBColor[0.15,0.45,0.8];ink=LightDarkSwitched[Black,White];Graphics[{{Directive[angleColor,Opacity[0.2]],Disk[observer,(3/5),{0,theta}]},{angleColor,AbsoluteThickness[2.5],Circle[observer,(3/5),{0,theta}]},{ink,AbsoluteThickness[2],Line[{observer,observer+{(18/5),0}}],Line[{observer,point}]},{angleColor,PointSize[0.018],Point[{observer,point}]},{ink,Text[Style["O",Italic],observer+{-(1/5),-(1/20)}],Text[Style["P",Italic],point+{(1/5),(1/10)}]},{angleColor,Text["α",observer+(4/5) {Cos[(theta/2)],Sin[(theta/2)]}]}},BaseStyle->Directive[16,FontFamily->"Times"]]]