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Copyright © 2011 Pearson, Inc. 5.6 Law of Cosines Goal: Apply the Law of Cosines.
Copyright © 2011 Pearson, Inc. Slide 5.6 - 2 What you’ll learn about Solving Triangles (SAS, SSS) Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.
Copyright © 2011 Pearson, Inc. Slide 5.6 - 3 Law of Cosines
Copyright © 2011 Pearson, Inc. Example: Solving a Triangle Solve the triangle. Slide 5.6 - 4
Copyright © 2011 Pearson, Inc. Example: Solving a Triangle Solve the triangle. Slide 5.6 - 5
Copyright © 2011 Pearson, Inc. A New Area Formula!
Copyright © 2011 Pearson, Inc. Slide 5.6 - 7 Area of a Triangle
Copyright © 2011 Pearson, Inc. SAS Area Example #1 The diagram at the right shows a triangular playground that is bounded by Main Street, High Street, and Central Street. The Park District has hired a contractor to pave the surface of the playground with asphalt. What is the area of the playground to the nearest foot?
Copyright © 2011 Pearson, Inc. SAS Area Example #2 Two adjacent sides of a triangle are 4cm and 6cm in length, the angle between them is 76°. Find the area of the triangle to the nearest thousandth.
Copyright © 2011 Pearson, Inc. 5.6 Law of Cosines.
Section Law of Cosines. Law of Cosines: SSS or SAS Triangles Use the diagram to complete the following problems, given triangle ABC is acute.
Copyright © 2011 Pearson, Inc. 5.5 Law of Sines Goal: Solve triangles that have no solution, one solution, or two solutions.
Copyright © 2011 Pearson, Inc. 5.5 Law of Sines. Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Deriving the Law of Sines Solving.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 1 Rational Numbers: Positive and Negative Decimals 5.
Quiz 13.5 Solve for the missing angle and sides of Triangle ABC where B = 25º, b = 15, C = 107º Triangle ABC where B = 25º, b = 15, C = 107º 1. A = ? 2.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
CHAPTER 5 LESSON 4 The Law of Sines VOCABULARY None.
Chapter 8 Section 8.2 Law of Cosines. In any triangle (not necessarily a right triangle) the square of the length of one side of the triangle is equal.
Copyright © 2009 Pearson Education, Inc. CHAPTER 8: Applications of Trigonometry 8.1The Law of Sines 8.2The Law of Cosines 8.3Complex Numbers: Trigonometric.
The Law of SINES.
Chapter 6 Additional Topics in Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc The Law of Cosines.
The Law of Sines. Quick Review Quick Review Solutions.
1 What you will learn How to solve triangles by using the Law of Cosines How to find the area of triangles if the measures of the three sides are given.
6.6 The Law of Cosines. 2 Objectives ► The Law of Cosines ► Navigation: Heading and Bearing ► The Area of a Triangle.
Notes Over 8.1 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles).
Law of Cosines. h a c A B C x D b - x b To derive the formula, fine the relationship between a, b, c, and A in this triangle. a 2 = (b – x) 2 + h 2 a.
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