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Lesson Plan
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\n\"Introduction\n\n
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\nWest Contra Costa Unified School District\n
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\nIntroduction to Trigonometric Functions\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nScholars first learn the definitions of the sine ratio, the cosine ratio, and the tangent ratio. After mastering these definitions, they use the new information to solve triangles.\n
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Interactive
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\n\"Determination\n\n
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\nCK-12 Foundation\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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Worksheet
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\n\"Leveled\n\n
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\nCurated OER\n
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\nLeveled Problem Solving Triangles\n

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\n\nFor Students\n\n4th - 6th\n
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\nIn this triangles practice worksheet, students sharpen their problem solving skills as they solve 6 story problems.\n
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Worksheet
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\n\"Using\n\n
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\nCurated OER\n
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\nUsing the Law of Sines and the Law of Cosines to Solve Triangles\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this trigonometry worksheet, students apply the Law of Sines and Cosines to solving for missing sides of a triangle. There are 5 questions with an answer key.\n
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Instructional Video4:22
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\n\"How\n\n
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\nCurated OER\n
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\nHow Do You Solve a Problem Using Indirect Measurement with Shadows?\n

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\n\nFor Teachers\n\n6th - 10th\n
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\nUsing indirect measurement, this video shows viewers how to find the height of a flagpole. The lecturer employs drawings as well as proportions to solve this problem, explaining each step. A useful resource to aid struggling learners and...\n
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Instructional Video4:57
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\n\"How\n\n
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\nCurated OER\n
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\nHow Do You Solve a Problem Using Indirect Measurement with Shadows?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nUsing indirect measurement, this video shows viewers how to find the height of a flagpole. The lecturer employs drawings as well as proportions to solve this problem, explaining each step. A useful resource to aid struggling learners and...\n
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\n\nGet Free Access\n\nSee Review\n
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Lesson Plan
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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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Lesson Plan
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\n\"Triangle\n\n
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\nCurated OER\n
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\nTriangle Inequality Theorem\n

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\n\nFor Teachers\n\n8th - 10th\n
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\nStudents use the inequality theorem to solve triangles and their properties. In this geometry instructional activity, students are given spaghetti of different lengths and asked to create triangles. They conclude the necessary length...\n
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Lesson Plan
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\n\"An\n\n
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\nCurated OER\n
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\nAn Application of Congruence\n

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\n\nFor Teachers\n\n9th - 10th\n
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\nStudents solve triangles using the properties if congruency. In this geometry lesson plan, students apply congruent and similar figures to solve real world and math problems. They show they are able to follow instructions.\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 worksheet, students use the laws of sines and cosines to solve triangles. The four page worksheet contains thirteen problems. Answers are not included.\n
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Instructional Video9:27
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\n\"Proof\n\n
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\nProof of the Law of Cosines, Trig Identities and Examples, Trigonometry\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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Instructional Video6:34
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: Law of Sines, Trig Identities and Examples, Trigonometry\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal proves the Law of Sines in this video by using the SOH-CAH-TOA model and setting up equivalent ratios.\n
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\n\"The\n\n
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\nEngageNY\n
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\nThe Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nPlaying with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...\n
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\n\"The\n\n
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\nEngageNY\n
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\nThe Angle-Angle (AA) Criterion for Two Triangles to Be Similar\n

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\n\nFor Teachers\n\n9th - 10th\n\nStandards\n
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\nWhat do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...\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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\n\"Applying\n\n
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\nEngageNY\n
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\nApplying the Laws of Sines and Cosines\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nBreaking the law in math doesn't get you jail time, but it does get you a wrong answer! After developing the Law of Sines and Cosines in lesson 33 of 36, the resource asks learners to apply the laws to different situations. Pupils must...\n
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Lesson Plan
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\n\"Sine\n\n
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\nEngageNY\n
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\nSine and Cosine of Complementary Angles and Special Angles\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nBuilding trigonometric basics here will last a mathematical lifetime. Learners expand on the previous lesson in a 36-part series by examining relationships between the sine and cosine of complementary angles. They also review the...\n
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Lesson Plan
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\n\"Algebra\n\n
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\nCurated OER\n
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\nAlgebra 2 & Trigonometry Practice: Law of Sines\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nIn this law of sines worksheet, students solve 9 multiple choice and short answer problems.  Students use the law of sines to missing side lengths and angles of triangles.\n
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Interactive
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\n\"Law\n\n
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\nCurated OER\n
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\nLaw of Sines or Sine Rule\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn this online math worksheet, high schoolers construct triangles and squares by utilizing the sine rule. This excellent resource allows the students to check their answers, and to get \"hints\" should they run into difficulties. A...\n
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Lesson Plan
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\n\"Using\n\n
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\nUsing Trigonometry\n

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\n\nFor Teachers\n\n5th\n
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\nFifth graders explore the use of trigonometry to find unknown sides and angles in right-angled triangles, taking the concepts that were developed in the previous unit and looking at different ways of practicing the new skills. Students...\n
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Activity
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\n\"Math\n\n
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\nMath Is Fun\n
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\nMath Is Fun: Solving Triangles\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nFind guidelines to help you \"solve\" triangles, which means finding the value of missing sides and angles. Provided are examples of six scenarios in which you can solve a triangle's missing measurements, as well as relevant equations,...\n
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Interactive
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\n\"Learn\n\n
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\nGovernment of Alberta\n
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\nLearn Alberta: Math Interactives: Exploring and Solving Triangles\n

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\n\nFor Students\n\n6th - 8th\n\nStandards\n
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\nThis multimedia Learn Alberta math resource focuses on the many triangles that are found in our everyday environment. The accompanying interactive component asks students to find triangles in a picture and to solve for the missing angles...\n
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Activity
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\n\"Trig\n\n
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\nTrig Without Tears: Solving Triangles\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis page provides a good explanation of how to solve oblique triangles (triangles containing no right angles.) The Law of Cosines section is about halfway of the way down the page.\n
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Solve Triangles Using the Law of Cosines\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nSolve missing triangle measures using the law of cosines. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.\n
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