Trigonometry and Oblique Triangle
MA1310 College Mathematics II LESSON PLAN WEEK 5
Dr. Tonjes September 2011
LESSON: Oblique Triangles, Laws of Sines and Cosines
INTRODUCTION: Student will demonstrate how to apply laws of sines and cosines to oblique triangles.
OBJECTIVES:
After completing this unit, the student will be able to:
6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems.
6.1. Summarize the Law of Sines.
6.2. Find the area of an oblique triangle using the sine function.
6.3. Judge when an ambiguous case of the Law of Sines occurs.
6.4. Solve applied problems using the Law of Sines.
6.5. Summarize the Law of Cosines.
6.6. Use the Law of Cosines to solve oblique triangle problems.
6.7. Solve applied problems using the Law of Cosines.
6.8. Find the area of an oblique triangle using Heron’s formula.
PROCEDURE:
Content
Activity
Objectives
Present objectives and purpose of lesson.
Law of Sines and Law of Cosines
Generalize the sine and cosine relations of the right triangles to oblique triangles by defining the two laws.
Law of Sines: This law relates the three sides of any triangle to the angles opposite the sides, typically labeled a, b, and c for the sides and A, B, and C for the angles.
Law of Cosines: This law relates one side to the other two sides and its corresponding angle:
Relate that either of these relations reduce to simpler forms for the case of right triangles, particularly:
1. Law of Sines reduces to c = c = c.
2. Law of Cosines reduces them to the Pythagorean Theorem.
Solving Oblique Triangles
Explore the types of triangles and how to solve them.
All oblique triangles make full use of the sum of angles rule that A + B + C = 180º in all triangles. All other elements require select application of the Law of Sines or Law of Cosines.
Types of Triangles
Right Triangles
Explain that a right triangle is solved when all three sides and the two free angles are all given measurements. As long as two sides or a side and
Dr. Tonjes September 2011
LESSON: Oblique Triangles, Laws of Sines and Cosines
INTRODUCTION: Student will demonstrate how to apply laws of sines and cosines to oblique triangles.
OBJECTIVES:
After completing this unit, the student will be able to:
6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems.
6.1. Summarize the Law of Sines.
6.2. Find the area of an oblique triangle using the sine function.
6.3. Judge when an ambiguous case of the Law of Sines occurs.
6.4. Solve applied problems using the Law of Sines.
6.5. Summarize the Law of Cosines.
6.6. Use the Law of Cosines to solve oblique triangle problems.
6.7. Solve applied problems using the Law of Cosines.
6.8. Find the area of an oblique triangle using Heron’s formula.
PROCEDURE:
Content
Activity
Objectives
Present objectives and purpose of lesson.
Law of Sines and Law of Cosines
Generalize the sine and cosine relations of the right triangles to oblique triangles by defining the two laws.
Law of Sines: This law relates the three sides of any triangle to the angles opposite the sides, typically labeled a, b, and c for the sides and A, B, and C for the angles.
Law of Cosines: This law relates one side to the other two sides and its corresponding angle:
Relate that either of these relations reduce to simpler forms for the case of right triangles, particularly:
1. Law of Sines reduces to c = c = c.
2. Law of Cosines reduces them to the Pythagorean Theorem.
Solving Oblique Triangles
Explore the types of triangles and how to solve them.
All oblique triangles make full use of the sum of angles rule that A + B + C = 180º in all triangles. All other elements require select application of the Law of Sines or Law of Cosines.
Types of Triangles
Right Triangles
Explain that a right triangle is solved when all three sides and the two free angles are all given measurements. As long as two sides or a side and