Revision #583 → #1350 · back to history
addedLaw of cosinesaf86a064b8b7
addedReduction to Pythagorean theorem1e626cc4f982
addedThird side from two sides and included anglee15f26deb63e
addedAngles from three sides37218d7ca148
addedThird side from two sides and non-included angle166692d5205c
addedNumber of solutions of SSA quadratic37223641b5ba
addedEuclid's Proposition II.12 (obtuse case)9261dac55466
addedEuclid's Proposition II.13 (acute case)4560dd848b2f
addedAl-Kāshī's formula (acute case)80419e015ac0
addedAl-Kāshī's formula (obtuse case)40dbf0b2210f
addedDerivation of law of cosines via squaringcbf7e34787ae
addedPythagorean theorem applied to triangle AHBc0501a040649
addedPythagorean theorem applied to triangle CHBe3032a9229dc
addedEuclid's Proposition 12 derivation951c06d49812
addedProof of acute case via Pythagorean theorem6b29bd42d377
addedSecond angle from two sides and included anglea051289c1c1a
addedAltitude decomposition of side cdfb446d44ade
addedMultiplying by c yields side relation2733fdbd72e4
addedAnalogous equations for other sides9990dfccaac8
addedLaw of cosines via subtraction of altitude equations2b6c3c2f3f5f
addedDistance formula for third sidee3c49b92b44e
addedLaw of cosines via Cartesian coordinates0592beb8c8d1
addedConstruction for Ptolemy proof544573ad40f0
addedLaw of cosines via Ptolemy's theorem2718da346701
addedPythagorean theorem as special case via Ptolemy0f442198c425
addedAcute case area equality19319a12ef88
addedObtuse case area equality7df787ca984d
addedPythagorean theorem on yellow triangle (acute, a>2b cos γ)a89ed9f9d8bb
addedTangent-secant theoremf12594d2b8c2
addedLaw of cosines via tangent-secant531f8e5792c5
addedPythagorean theorem applied (acute, a<2b cos γ)a794a90e091d
addedChord theoremd25a807b0ca3
addedLaw of cosines via power of point (obtuse)0634b14fe7dd
addedAngle sum identities for sine and cosine7da712af266a
addedDerived identity via Pythagorean trigonometric identitye27d046bd007
addedLaw of sinesdbb1aade1c7e
addedLaw of cosines via multiplication by side squared99316cb56024
addedDot product proof of law of cosinesbc3c986d9c99
addedIsosceles simplification of law of cosinesa8d052f7fe9f
addedLaw of cosines for tetrahedraa17c4e1faa0e
addedSmall-angle (haversine-like) form of law of cosines0e8f77f5b2a1
addedInfinitesimal limit yields arc length formula3adf3a0c5245
addedSpherical law of cosines92f787431265
addedHyperbolic law of cosines (first)be9d68c608a9
addedHyperbolic law of cosines (second)21149d62f5fc
addedHyperbolic side lengths from anglese19961880f3f
addedGeneralization to polyhedraa9cbe1002af8