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Summary Of: Law of cosines

This article is about the law of cosines in Euclidean geometry... The law of cosines is useful for computing the third side of a triangle when two sides and their... This formula may be transformed into the law of cosines by noting that... and provided the first explicit statement of the law of cosines in a form suitable for... the law of cosines is still referred to as the... modern algebraic notation allowed the law of cosines to be written in its current symbolic form... the law of cosines by applying can be deduced by using the Pythagorean theorem only... Now the law of cosines is rendered by a straightforward application of Ptolemy... Proof of the law of cosines for acute angle... Proof of the law of cosines for acute angle... Proof of the law of cosines for acute angle... Proof of the law of cosines for obtuse angle... Proof of the law of cosines for obtuse angle... Proof of the law of cosines for obtuse angle... yielding a proof of the law of cosines in the case that the angle... Proof of the law of cosines using the power of a point theorem... Proof of the law of cosines using the power of a point theorem... Proof of the law of cosines using the power of a point theorem... The law of cosines is equivalent to the formula... The law of cosines formulated in this context states...

Encyclodia Page On: Law of cosines

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Fig. 1 - A triangle. | | Trigonometry | History | Usage | Functions | Inverse functions | Further reading | List of identities | Exact constants | Generating trigonometric tables | CORDIC | Euclidean | Law of sines | Law of tangents | Pythagorean theorem | Calculus | Trigonometric integral | Trigonometric substitution | Integrals of functions | Derivatives of functions | Integrals of inverses | spherical geometry | law of cosines (spherical) | Lambert's cosine law | trigonometry | Al-Kashi | triangle | cosine | angles | Pythagorean theorem | right triangles | ° | Fig. 2 - Obtuse triangle ABC with perpendicular BH | | cosine | Euclid | Elements | Thomas L. Heath | trigonometry | Middle Ages | Muslim mathematicians | Persian astronomer | al-Battani | spherical geometry | al-Kashi | Samarqand | triangulation | France | Western world | François Viète | Fig. 3 - Applications of the law of cosines: unknown side and unknown angle. | | triangulation | Pythagorean theorem | right triangle | round-off errors | floating point | quadratic equation | congruence | Fig. 4 - An acute triangle with perpendicular | | perpendicular | trigonometry | Fig. 5 - Obtuse triangle ABC with height BH | | Euclid | Pythagorean theorem | Expanding | Elements | Fig. 6 - A short proof using trigonometry for the case of an acute angle | | Ptolemy's theorem | Proof of law of cosines using Ptolemy's theorem | | cyclic quadrilateral | areas | parallelogram | parallelogram | Fig. 7a - Proof of the law of cosines for acute angle γ by "cutting and pasting". | heptagon | congruent | Fig. 7b - Proof of the law of cosines for obtuse angle γ by "cutting and pasting". | hexagon | congruent | congruent triangles | geometry of the circle | geometric | Pythagorean theorem | Algebraic | binomial theorem | Fig. 8a - The triangle ABC (pink), an auxiliary circle (light blue) and an auxiliary right triangle (yellow) | | perpendicular | right triangle | isosceles triangle | circle | tangent | here | Pythagorean theorem | tangent secant theorem | secant | power | power of a point theorem | Fig. 8b - The triangle ABC (pink), an auxiliary circle (light blue) and two auxiliary right triangles (yellow) | | perpendicular | right triangle | isosceles triangle | circle | chord | Pythagorean theorem | chord theorem | Fig. 9 - Proof of the law of cosines using the power of a point theorem. | secant | power | negative numbers | vectors | dot product | lengths | angle | Fig. 10 - Vector triangle | | isosceles | tetrahedron | dihedral angles | Triangulation | Law of sines | Law of tangents | Law of cosines (spherical) | 1889 | cut-the-knot | Categories | Trigonometry | Angle | Triangle geometry | Articles containing proofs |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Law of cosines".