Theorems · Theorem · geometry

EuclideanGeometry.oangle_left_eq_arctan_of_oangle_eq_pi_div_two

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₂ p₃ : P},
  EuclideanGeometry.oangle p₁ p₂ p₃ = ↑(Real.pi / 2) →
    EuclideanGeometry.oangle p₃ p₁ p₂ = ↑(Real.arctan (dist p₃ p₂ / dist p₁ p₂))

An angle in a right-angled triangle expressed using arctan.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle

Cited by

0 results in Mathlib

Foundations

Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented