Theorems · Theorem · geometry

EuclideanGeometry.angle_eq_arcsin_of_angle_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] {p₁ p₂ p₃ : P},
  EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi / 2 →
    p₁ ≠ p₂ ∨ p₃ ≠ p₂ → EuclideanGeometry.angle p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃)

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

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle

Cited by

3 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor