Classic Math Proofs of the Law of Sines and the Law of Cosines
by Steve Chow · blackpenredpen (YouTube)
Eleven-minute blackboard derivation of both laws in one sitting, dropping altitudes in an oblique triangle and handling the obtuse configuration rather than asserting the formulas. Builds the geometric reason the ratios hold before any problem-solving.
More resources on Law of Sines & Cosines
Trigonometry Khan Academy
Master law of sines & cosines with Sal Khan's free Trigonometry course! Ace triangles & trigonometry calculations.
The Laws of Sines and Cosines
Reference page collecting classical proofs of both laws: Euclid's Elements II.12 treatment of the obtuse case, two proofs without words from Nelsen using power of a point and Ptolemy's theorem, Maor's projection argument, and dissection proofs.
Precalculus (Stitz-Zeager), Section 11.3: The Law of Cosines
Companion section deriving the Law of Cosines by placing a triangle at the origin and applying the distance formula, covering the SAS and SSS cases and continuing to Heron's formula. Twenty-seven applied exercises with complete answers.
Precalculus (Stitz-Zeager), Section 11.2: The Law of Sines
Open-textbook section proving the Law of Sines separately for acute, obtuse, and right triangles, then systematizing the ambiguous SSA case into zero, one, or two triangles. Includes bearing and navigation applications and 38 answered exercises.
mathsisfun.com
MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes.