The relation of led lens angle and illuminate area

The angle of lens is decision illuminate direction, we can calculate illuminate area with tangent function.
angle
Trigonometric  Function  Of  Acute Angle

tan10°=0.176(can calculate that lens value as 20°)
tan12.5°=0.222(can calculate that lens value as 25°)
tan15°=2-√3
tan22.5°=√2-1
tan30°=√3/3
tan45°=1
tan60°=√3

Different angle , different aperture and illuminate value

30°
1meter aperture φ0.56M illuminate area as 0.246 square   metres
2meter aperture φ1.12M illuminate area as 0.985 square metres
3meter aperture φ1.68M illuminate area as 2.217 square metres
45°
1meter aperture φ0.828M illuminate area as 0.538 square metres
2meter aperture φ1.656M illuminate area as 2.154 square metres
3meter aperture φ2.484M illuminate area as 4.864 square metres
60°
1meter aperture φ1.15M illuminate area as 1.046 square metres
2meter aperture φ2.3M illuminate area as 4.189 square metres
3meter aperture φ3.46M illuminate area as 9.424 square metres
120°
1meter aperture φ3.464M illuminate area as 9.424 square metres
2meter aperture φ6.928M M illuminate area as 37.697square metres
3meter aperture φ10.392M illuminate area as 84.818 square metres