Lesson 4: 6.5 & 6.6 The Laws of Sines and Cosines

What is the Law of Sines, and how is it used to solve oblique triangles?

What is the Law of Cosines, and how is it used to solve oblique triangles?

What are the ambiguous cases of the Law of Sines, and how can we identify and solve them?

Law of sines, law of cosines, oblique triangles, ambiguous

HS.MA.4C - 4C. Define trigonometric ratios, solve problems involving right triangles, and apply them in real world situations

By the end of this lesson, students will be able to apply the Law of Sines and the Law of Cosines to solve a variety of oblique triangle problems. They will also be able to identify and solve ambiguous cases of the Law of Sines and use these laws to solve real-world problems.

Purpose: Students will develop a deep understanding of the Law of Sines and the Law of Cosines and apply these laws to solve oblique triangles.

DOK Level: 3 (Strategic Thinking)

Surveying: A surveyor wants to measure the distance across a river. They can use the Law of Sines or Law of Cosines to calculate the distance based on measured angles and distances.

Navigation: A pilot needs to determine the distance between two cities. They can use the Law of Cosines to calculate the distance based on the latitude and longitude of the two cities.

Students may mistakenly apply the Law of Sines or the Law of Cosines when the incorrect law is needed.

Students may struggle to identify and solve ambiguous cases of the Law of Sines.

Students may make errors when using calculators to solve trigonometric equations.

Use diagrams and models to help students visualize the concepts.

Provide clear, step-by-step examples to guide students through the problem-solving process.

Relate the laws to real-world applications to make the concepts more meaningful.

Do Now Questions

Exit Slips

Quizzes

Textbook and supplementary materials in class

Google Classroom for notes and how-to videos