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# Topic: Law of cosines

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 Law of cosines - Wikipedia, the free encyclopedia In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) is a statement about a general triangle which relates the lengths of its sides to the cosine of one of its angles. The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known. It was not until the development of modern trigonomotry in the middle ages by muslim mathematicians that the law of cosines evolved beyond Euclid's two theorems. en.wikipedia.org /wiki/Law_of_cosines   (1773 words)

 Law of tangents: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-11-07) In trigonometry, the law of sines (or sine law) is a statement about arbitrary triangles in the plane.... In trigonometry, the law of cosines is a statement about arbitrary triangles which generalizes the pythagorean theorem by correcting it with a term proportional... (the law of cosines is a statement about arbitrary triangles which generalizes the pythagorean theorem by correcting it with a term proportional... www.absoluteastronomy.com /encyclopedia/l/la/law_of_tangents.htm   (623 words)

 Law of cosines 1 - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-07) Start the Law of cosines 1 article or add a request for it. Look for Law of cosines 1 in Wiktionary, our sister dictionary project. Look for Law of cosines 1 in the Commons, our repository for free images, music, sound, and video. www.sciencedaily.com /encyclopedia/law_of_cosines_1   (161 words)

 Law of Cosines The law of cosines for calculating one side of a triangle when the angle opposite and the other two sides are known. It has application along with the law of sines to the problem of the heading angle for an aircraft in the wind. With that angle and the law of sines, the offset angle hyperphysics.phy-astr.gsu.edu /hbase/lcos.html#c1   (250 words)

 Word Problems: Law of Cosines A typical problem that requires the use of the Law of Cosines in order to solve it involves a triangle in which there is no right angle. The Law of Cosines for a triangle ABC is stated below, assuming that the side opposite angle A is a, the side opposite angle B is b, and the side opposite angle C is c: Use of the Law of Cosines involves a simple equation, but the solution may involve the use of the quadratic formula. www.algebralab.org /Word/Word.aspx?file=Trigonometry_LawCosines.xml   (537 words)

 Law of Cosines The law of cosines is best thought of as an extension of the Pythagorean Theorem, with a term that adjusts if the included angle is not a right angle. LAW OF COSINES is found in 1895 in Plane and spherical trigonometry, surveying and tables by George Albert Wentworth: "Law of Cosines. There is a Law of Cosines for the sides and another for the angles. www.pballew.net /lawofcos.htm   (651 words)

 The Law of Cosines The Law of Cosines is a generalization of the Pythagorean Theorem. The Law of Cosines may be used to solve triangles of type SAS and SSS. There is an alternate form of the Law of Cosines which is used to solve the SSS case. jwbales.home.mindspring.com /precal/part6/part6.2.html   (634 words)

 Law of Cosines   (Site not responding. Last check: 2007-11-07) The law of cosines can be used when two sides and the included angle are known or when all three sides are known. You can use the law of cosines to solve the ambiguous case that we looked at with the law of sines. The trick is to write the law of cosines as a quadratic in terms of the unknown side. www.lhs.logan.k12.ut.us /~rweeks/trig/law_of_cosines.htm   (316 words)

 Law of Cosines and Law of Sines for Triangles   (Site not responding. Last check: 2007-11-07) Law of Cosines and Law of Sines for Triangles Laws of Cosines and Sines for Angles/Sides of Triangles Enter two angles and any side, or 3 sides, or two sides and angle between them, into the boxes above to get the other sides and angles using the laws of cosines or sines and sum of angles of triangle. www.wcrl.ars.usda.gov /cec/java/triangle.htm   (96 words)

 Law of cosines - Hutchinson encyclopedia article about Law of cosines The cosine rule is a rule of trigonometry that relates the sides and angles of triangles. It can be used to find an unknown length or angle in a triangle. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional. encyclopedia.farlex.com /Law+of+cosines   (126 words)

 The Laws of Sines and Cosines Another important relationship between the side lengths and the angles of a triangle is expressed by the Law of Cosines. The essence of the Law of Cosines has been known to Euclid, who proved the obtuse case as II.12 and the acute case as II.13. (This is in fact the same proof as we used to show that the law of cosines is a direct consequence of a less general Pythagorean theorem. www.cut-the-knot.org /pythagoras/cosine2.shtml   (692 words)

 The Law of Cosines The Law of Cosines (interchangeably known as the Cosine Rule or Cosine Law) is a generalization of the Pythagorean Theorem in that a formulation of the latter can be obtained from a formulation of the Law of Cosines as a particular case. Thus, in the course of the proof of the Cosine Rule one proves directly the Pythagorean Theorem. Also, the cosines law admits a slightly different form discovered by Larry Hoehn that generalizes the Pythagorean theorem in a somewhat different way. www.cut-the-knot.org /pythagoras/cosine.shtml   (531 words)

 Using the Law of Sines and Law of Cosines Using the Law of Sines and the Law of Cosines Use the Law of Cosines to determine side c. The analysis of the Ambiguous Case was taken from a letter to The Mathematics Teacher by Carolyn J. Case, Vincennes University, Vincennes, IN. www.pen.k12.va.us /Div/Winchester/jhhs/math/lessons/trig/flowchrt.html   (216 words)

 law of cosines / All About Law Law of Cosines -- from MathWorld Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of cosines statesSolving for the cosines yields the equivalent... The Law of Cosines (interchangeably known as the Cosine Rule or Cosine Law) is a generalization of the Pythagorean... law of sines and law of cosines www.warley-mrc.org /law-of-cosines   (282 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-11-07) When you have a triangle which is not right, the closest analogue is something called the Law of Cosines. If the angle is other than 90 degrees; however, the cosine of C is not zero. For example, if the angle C is 60 degrees, its cosine is 1/2, and you get the equation c^2 = a^2 +b^2 - a*b. mathforum.org /library/drmath/view/55005.html   (221 words)

 Topics in trigonometry:  The law of cosines WE USE THE LAW OF COSINES to solve triangles that are not right-angled. In particular, when we know two sides of a triangle and their included angle, then the Law of Cosines enables us to find the third side. b² = a² + c² − 2ac cos B. This is the Law of Cosines. www.themathpage.com /aTrig/law-of-cosines.htm   (459 words)

 The Law of Cosines   (Site not responding. Last check: 2007-11-07) The Pythagorean theorem is basically a generalization of the Law of Cosines. The Law of Cosines is used in any triangle when given three sides (SSS) or two sides and their included angle (SAS). This is one form of the Law of Cosines. www.ms.uky.edu /~lee/ma502/pythag/cos.htm   (151 words)

 Law of Sines and Cosines   (Site not responding. Last check: 2007-11-07) It does, and we'll demonstrate this by proving the law of cosines algebraically and geometrically. Thus the law of cosines, a generalization of the Pythagorean theorem, is valid when angles are defined as above. Given the law of cosines, prove the law of sines by expanding sin(θ) www.mathreference.com /la,law.html   (296 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-11-07) Date: Fri, 18 Aug 1995 17:24:28 +1000 From: Tony Snell Subject: Mathmatical proof, cosine rule G'day, I have been given this problem solving project. Prove that, in any triangle, the sum of the squares of two sides is equal to twice the square on half the third side plus twice the square on the line joining the midpoint of the third side to its opposite vertex (Hint: You may find the cosine rule useful). I know have to prove the left hand side equals the right hand side of the equation and use a variant of the cosine rule to prove the equation, but how? mathforum.org /library/drmath/view/53963.html   (237 words)

 Trigonometry Law of Cosines We can't use the Law of Sines from the last chapter on this one. That means we COULD use the Law of Sines to find the rest of the missing info. I guess since there was a cosine in the equation that made sense. www.math-prof.com /Trig/Trig_Ch_06.asp   (890 words)

 Law of Cosines We have derived the law of Cosines for side a.  It has three forms which are useful: The law of cosines is useful when given two sides and an included angle (SAS) Now use the law of sines and find the smallest angle.  The smallest angle is definitely an acute angle.  The law of sines can not distinquish between acute and obtuse because both angles give a positive answer. home.alltel.net /okrebs/page94.html   (427 words)

 KR Mathematics: Derivations of the Law of Sines and Cosines   (Site not responding. Last check: 2007-11-07) KR Mathematics: Derivations of the Law of Sines and Cosines And finally we have the Law of Cosines. You are in KR > Mathematics > Derivations of the Law of Sines and Cosines www.kopernekus.com /math/derivation_sincos.asp   (119 words)

 Keymath.com : Discovering Geometry : JavaSketchpad™ Activities : Law of Cosines You can use the Law of Cosines to solve for unknown measures in a triangle when you are given three side lengths, or two side lengths and the measure of the included angle. This sketch shows how the Law of Cosines can be derived for a triangle when angle A is obtuse and angles B and C are acute. This is the Law of Cosines for triangle ABC. www.keymath.com /DG/dynamic/law_of_cosines.html   (290 words)

 Law Of Cosines   (Site not responding. Last check: 2007-11-07) So the talent of "knowing" the law of cosines is to (1) know the Pythagorean Theorem and (2) use it to quickly derive the law of cosines. Maybe, but it's the sort of thing you can practice to the point where you can do it in less than a minute whenever you need it. More about the Law of Cosines can be found here. mcraefamily.com /MathHelp/GeometryCosines.htm   (327 words)

 Euclid's Elements, Book II, Proposition 12 This conclusion is very close to the law of cosines for oblique triangles. Trigonometry was developed some time after the Elements was written, and the negative numbers needed here (for the cosine of an obtuse angle) were not accepted until long after most of trigonometry was developed. Nonetheless, this proposition and the next may be considered geometric versions of the law of cosines. aleph0.clarku.edu /~djoyce/java/elements/bookII/propII12.html   (313 words)

 Law of Sines & Law of Cosines You and your team are assigned the task of designing a web page to help yourselves and other students learn about the 'Law of Sines'. This means 10 for the Law of Sines. State the what topics you learned last year in Sequential II and the year before in Sequential I, that are necessary knowledge in order to you to learn and understand the 'Law of Sines' topic. www.bellmore-merrick.k12.ny.us /webquest/math/sines.html   (771 words)

 PlanetMath:   (Site not responding. Last check: 2007-11-07) law of cosines (=cosines law) owned by drini law of signs under multiplication in a ring owned by alozano law of sines (=sines law) owned by drini planetmath.org /encyclopedia/L   (2042 words)

 Law of cosines   (Site not responding. Last check: 2007-11-07) I missed a few days of class and I can't figure out how to solve Law of Cosines problems. I have the notes and formulas but I can't figure out how to do the math involved to answer the problems. I am also getting confused about how to use degrees and seconds in the Law of Sine and Cosine. mathcentral.uregina.ca /QQ/database/QQ.09.00/emily1.html   (139 words)

 cosine's law   (Site not responding. Last check: 2007-11-07) The Law of Cosines is the relationship between sides and angles in any triangle. Draw a triangle ABC,then draw three squares sharing their sides with the triangle ABC. KOBAYASHI Akira at Seisan Circle(a math education research group) told us the idea of the applet. www.ies.co.jp /math/java/trig/yogen1/yogen1.html   (96 words)

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