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Law of Cosines Lesson Plan

Instructor: Matt Gromlich

Matt has taught at the K-12 level and beyond for the last five years. He is currently getting his Ph.D. in Mathematics Education.

This lesson plan introduces the Law of Cosines to students and helps them contextualize this concept by using the Pythagorean Theorem as a basis. A pre-activity reinforces students' previous knowledge of the Pythagorean Theorem, and a post-activity uses student modeling of problems to show conceptual understanding. Throughout the lesson, discussion questions are presented to build upon student's prior knowledge and extend student learning.

Learning Objectives:

Upon completion of this lesson, students will be able to:

  • Identify an oblique triangle.
  • Reproduce the Law of Cosines.
  • Use the Law of Cosines to find the missing side of an oblique triangle, given two other sides and the opposite angle.
  • Use the Law of Cosines to find the missing angle of an oblique triangle, given all three sides.

Grade Level

High school Geometry, Trigonometry, or Algebra 2

Length

50-70 minutes

Curriculum Standards

CCSS.Math.Content.HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

CCSS.Math.Content.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CCSS.Math.Content.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Materials

  • Worksheet (either printed or projected for students)
  • Pythagorean Theorem worksheet, textbook problems, or related lessons (for pre-activity)
  • Additional Law of Cosines worksheet, textbook problems, or related lessons (for post-activity)

Pre-Lesson Review Activity

  1. This activity can be completed by teams, partners, or individual students.
  2. Have students solve Pythagorean Theorem problems from a worksheet, the textbook, or related lessons.
  3. Choose or create problems that make the students solve for different sides (i.e. not always finding the hypotenuse).
  4. Assign students a specific problem for them to be 'experts' on.
  5. Have students present their problem, explaining their thought process, their steps, and how they know their answer is correct in the context of the problem.

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