EuclideanGeometry.dist_div_sin_oangle_left_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) → dist p₃ p₂ / (EuclideanGeometry.oangle p₃ p₁ p₂).sin = dist p₁ p₃A side of a right-angled triangle divided by the sine of the opposite angle equals the hypotenuse.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Real.pistatement and proof · cited by 1,774
- Module.finrankstatement and proof · cited by 1,770
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- Real.Anglestatement and proof · cited by 518
- Real.sinproof · cited by 389
- Real.Angle.coestatement and proof · cited by 360
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.