Theorems · Theorem · geometry

EuclideanGeometry.angle_eq_arccos_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 →
    EuclideanGeometry.angle p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃)

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

Defined in: Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
Cited by: 2 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace MetricSpace NormedAddTorsor

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Cites23

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
Norm.normproof · cited by 5,413
InnerProductSpacestatement and proof · cited by 3,523
Real.pistatement and proof · cited by 1,774
MetricSpacestatement and proof · cited by 1,684
Dist.diststatement and proof · cited by 1,539
add_commproof · cited by 1,535
NormedAddTorsorstatement and proof · cited by 1,325
Inner.innerproof · cited by 1,089
VSub.vsubproof · cited by 817
EuclideanGeometry.anglestatement and proof · cited by 187

Cited by2

Results whose statement or proof uses this declaration.

EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_twoproof · cited by 0
EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_twoproof · cited by 0