Theorems · Theorem · geometry

EuclideanGeometry.tan_angle_mul_dist_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 → Real.tan (EuclideanGeometry.angle p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ p₂

The tangent of an angle in a right-angled triangle multiplied by the adjacent side equals the opposite side.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle

Cited by

2 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor