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Instructional Video9:27
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\n\"Proof\n\n
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\nKhan Academy\n
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\nProof of the Law of Cosines, Trig Identities and Examples, Trigonometry\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal derives the Law of Cosines using a method similar to the wayward ship captain word problem he solves in another video. This video provides a good review of using the SOH-CAH-TOA model, the Pythagorean Theorem, some basic trig...\n
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\n\"Law\n\n
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\nEngageNY\n
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\nLaw of Cosines\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nBuild upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...\n
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Interactive
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\n\"Law\n\n
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\nCK-12 Foundation\n
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\nLaw of Cosines: Angles in the Outfield\n

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\n\nFor Students\n\n10th - 12th\n
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\nTake me out to the trig class. Individuals use an interactive to see how angles on a baseball field change as the position of two runners change. A set of challenge questions has them apply the Law of Cosines to solve problems.\n
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\n\"The\n\n
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\nCurated OER\n
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\nThe Law of Sines and the Law of Cosines\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn this college level trigonometry worksheet, students apply the Law of Sines and the Law of Cosines to solve triangles. The four page worksheet contains forty-four problems. Solutions are not provided. \n
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\n\"Putting\n\n
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\nEngageNY\n
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\nPutting the Law of Cosines and the Law of Sines to Use\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nUse the Law of Cosines and the Law of Sines to solve problems using the sums of vectors. Pupils work on several different types of real-world problems that can be modeled using triangles with three known measurements. In the process,...\n
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Interactive
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\n\"Law\n\n
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\nCK-12 Foundation\n
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\nLaw of Cosines: Baseball Diamond\n

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\n\nFor Students\n\n10th - 12th\n
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\nCatch a great resource! Individuals use an interactive that allows them to move players on a baseball field. They calculate distances between players using the Law of Cosines.\n
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Interactive
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\n\"Law\n\n
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\nCK-12 Foundation\n
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\nLaw of Cosines: Get on Base\n

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\n\nFor Students\n\n10th - 12th\n
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\nBaseball is all about math. Young baseball and mathematics enthusiasts determine the distance between players on a baseball field using the Law of Cosines. An interactive helps them find relevant distances and angles to use in their...\n
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Interactive
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\n\"Law\n\n
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\nCK-12 Foundation\n
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\nLaw of Cosines: Building a Zip Line\n

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\n\nFor Students\n\n10th - 12th\n
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\nZip this resource into your lesson plans. Here is an interactive that shows how angles and lengths change based on conditions for a zip line. Scholars use the Law of Cosines to solve problems in this context.\n
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Worksheet
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\nA Different Proof of the Law of Cosines\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this proofs worksheet, students construct 1 proof of the law of cosines.  Students construct a right triangle within a circle to  prove the law of cosines.\n
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Interactive
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\n\"Identify\n\n
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\nCK-12 Foundation\n
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\nIdentify Accurate Drawings of Triangles: Law of Cosines\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nDrawing triangles is easy, even if you have to calculate the exact length of its sides. Scholars use the Law of Cosines to find missing sides of triangles. An interactive helps them check their answers.\n
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\n\"Law\n\n
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\nLaw of Cosines Practice\n

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\n\nFor Teachers\n\n8th - 10th\n
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\nStudents practice solving problems with non-right triangles. In this precalculus lesson, students define and identify the properties of the Law of Cosine. They solve problems and investigate the history behind Cosine.\n
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\n\"Law\n\n
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\nLaw of Cosines Word Problem\n

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\n\nFor Teachers\n\n10th - 11th\n
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\nStudents solve problems using the law of cosines. In this precalculus lesson, students meet different criteria as they solve problems. They apply the formula for cosines to solve word problems.\n
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Instructional Video2:52
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\n\"Sine\n\n
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\nSine or Cosine Rule?\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nExplore triangle problems that require the Law of Sine or Law of Cosine. A straightforward lesson focuses on deciding when to use each law. The instructor presents several triangles for pupils to consider and describes patterns in the...\n
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\n\"Concepts\n\n
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\nCurated OER\n
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\nConcepts in Precalculus 1: Trigonometry\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents investigate trigonometry.  In this Algebra II/Pre-calculus/Trigonometry lesson, students explore Islamic achievements in mathematics as they calculate angles and distances using the Law of Sines and the Law of...\n
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\nSection 6.1-6.2 Precalculus: Trigonometry\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this trigonometry worksheet, students solve 15 triangle problems.  Students use the law of sines and law of cosines to find the missing angles and side lengths of a triangles.\n
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Worksheet
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\n\"Law\n\n
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\nLaw of Cosines\n

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\n\nFor Students\n\n10th\n
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\nIn this Law of Cosines worksheet, 10th graders solve 10 different problems related to applying the Laws of Cosine. First, they determine the length of a side rounded to the nearest integer. Then, students determine the largest angle of a...\n
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Worksheet
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\n\"Law\n\n
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\nCurated OER\n
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\nLaw of Sines and Law of Cosines\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this Pre-calculus/Trigonometry activity, students use the laws of sines and cosines to solve triangles. The four page activity contains thirteen problems. Answers are not included.\n
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\n\"Using\n\n
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\nEngageNY\n
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\nUsing Trigonometry to Find Side Lengths of an Acute Triangle\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nNot all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems. \n
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Assessment
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\n\"End-of-Module\n\n
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\nEngageNY\n
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\nEnd-of-Module Assessment Task - Geometry (module 2)\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nIncrease the level of assessment rigor with the test of performance tasks. Topics include similar triangles, trigonometric ratios, Law of Sines, Law of Cosines, and trigonometric problem solving. \n
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Interactive
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\n\"Distance\n\n
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\nCK-12 Foundation\n
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\nDistance Between Two Polar Coordinates: Exploring Changes in Angle and Radius\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nGet straight answers on a curved grid. An interactive has learners apply the Law of Cosines to find the distance between two points on the polar coordinate plane. The pupils use the radii lengths and the angle between the two radii...\n
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Interactive
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\n\"Determination\n\n
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\nDetermination of Unknown Triangle Measures Given Area: Jib Sheets\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nSolving triangles is a breeze. Young boat enthusiasts solve problems involving triangles in the context of sails on a boat. They must apply different strategies, including the Law of Cosines and area formulas.\n
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\nSome More Trigonometry\n

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\n\nFor Teachers\n\n9th - 10th\n
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\nStudents define the law of cosine and its correct usage. In this trigonometry lesson, students define the law of Heron's area formula and use it to solve problems. They review other trigonometric values and identify the identities.\n
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\n\"Journey\n\n
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\nJourney of the Nez Perce\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nStudents study the retreat of the Nez Perce Native Americans into Montana while tracing their journey on a map. They use the law of cosines to solve problems based on the navigational methods of the Nez Perce. They work with both the law...\n
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Interactive
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\n\"Law\n\n
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\nLaw of Cosines\n

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\n\nFor Students\n\n9th - 12th\n
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\nFor this cosine worksheet, students will find the length of the third side of a triangle given the length of the other two side. Students will use the Law of Cosines to find the length of the missing side. Answers will be rounded to 3...\n
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