Orientation.norm_div_sin_oangle_sub_right_of_oangle_eq_pi_div_two
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [hd2 : Fact (Module.finrank ℝ V = 2)]
(o : Orientation ℝ V (Fin 2)) {x y : V}, o.oangle x y = ↑(Real.pi / 2) → ‖x‖ / (o.oangle y (y - x)).sin = ‖y - x‖A side of a right-angled triangle divided by the sine of the opposite angle equals the hypotenuse, version subtracting vectors.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
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.normstatement and proof · cited by 5,413
- 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
- Real.Anglestatement and proof · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Orientationstatement and proof · cited by 360
- SignTypeproof · cited by 318
- Orientation.oanglestatement and proof · cited by 205
Cited by1
Results whose statement or proof uses this declaration.
- Orientation.norm_div_sin_oangle_sub_left_of_oangle_eq_pi_div_twoproof · cited by 0