Sine law and cosine law
Drag the vertices of a triangle, switch between the sine law and the cosine law, and check the side-angle relations and the circumradius.
Sine law and cosine law
4 pieces about this concept, across works, topic guides, and exam visualizations.
Works
Exam visualizations
A 120° isosceles construction and the cosine law
112 AST Mathematics I, Fill-in 9: read the vertex angle and the base angles, then use an angle-sum formula and the cosine law for the squared distance between the new vertices.
Shortest path on a lampshade
2023 AMC 12B, Problem #21 unfolds the shade into a half-annulus, where the straight line leaves the paper and the shortest path is a tangent plus an inner arc.
Equilateral triangle on three concentric circles
2025 AMC 12B, Problem #25 turns the radius-2 circle 60° about a vertex so that it is internally tangent to the outer circle, and the squared side is 7.