Theorems · Theorem · geometry

Orientation.oangle_sub_right_eq_arcsin_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) → o.oangle y (y - x) = ↑(Real.arcsin (‖x‖ / ‖y - x‖))

An angle in a right-angled triangle expressed using arcsin, version subtracting vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle

Cited by

1 results in Mathlib

Foundations

Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact