Geometry, Trigonometry

Trigonometry studies the relationships between the angles and side lengths of triangles, especially right-angled triangles, using functions like sine, cosine, and tangent. Expected questions involve finding unknown angles or sides, solving trigonometric equations, and applying these concepts to various geometric problems.

• Question

  In space, there are 30 non-degenerate vectors. Prove that there are at least 2 such that the angle between them is no greater than 45 degrees. 
  A. Tulpigo

  Topics:

  Geometry -> Trigonometry Geometry -> Spherical Geometry Combinatorics -> Pigeonhole Principle Combinatorics -> Combinatorial Geometry Geometry -> Plane Geometry -> Angle Calculation Geometry -> Vectors
  Sources:
  • Tournament of Towns, 1979-1980, Main, Spring Question 4