Theorems · Theorem · geometry

Orientation.tan_oangle_sub_left_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 (x - y) x).tan = ‖y‖ / ‖x‖

The tangent of an angle in a right-angled triangle as a ratio of sides, version subtracting vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle

Cited by

0 results in Mathlib

Foundations

Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact