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Lesson 9.6 Apply the Law of Cosines

Lesson 9.6 Apply the Law of Cosines. Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up. Lesson Presentation. Lesson Quiz. Warm-Up. Solve ABC with and. SOLUTION. 1. Draw a p icture . 2 . Find the third angle,.

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Lesson 9.6 Apply the Law of Cosines

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  1. Lesson 9.6Apply the Law of Cosines Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up Lesson Presentation Lesson Quiz

  2. Warm-Up Solve ABC with and . SOLUTION 1. Draw a picture  2. Find the third angle, 3. Write the Law of Sine proportion 4. Write the Law of Sine proportion In ABC, and b.

  3. Warm-Up Solve ABC with and . SOLUTION 1. Evaluate SSA case, a b & is obtuse, One triangle 3. Write the Law of Sine proportion 4. Find the third angle, 5. Write the Law of Sine proportion In ABC, and a.

  4. Vocabulary Law of Cosines: Can be used to solve triangles with no right angle, when two sides and the included angle are known (SAS), or when all three sides are known. (SSS).

  5. Essential Understandings In which cases can the Law of cosines be used to solve a triangle? • The law of cosines is used to solve triangles with no right angle in the SAS and SSS cases.

  6. 1 EXAMPLE Solve a triangle for the SAS case Solve ABC with and . SOLUTION 1. Draw a picture  2. Apply the Law of Cosines 3. Apply the Law of Cosines 4. Apply the Law of Cosines In ABC, and .

  7. 2 EXAMPLE Solve a triangle for the SSS case Solve ABC with and . SOLUTION 1. Draw a picture  2. Apply the Law of Cosines 3. Use Law of Sines - SSAcase, a b & is obtuse, One Write the Law of Sine proportion 4. Find the 3rd angle, In ABC, and .

  8. 3 EXAMPLE Write and Solve a real – Use trig to find area of triangle The lengths of the sides of a plot of land are 120 ft., 150 ft., and 175 ft. Find the largest angle of the triangle. SOLUTION 1. Draw a picture  2. Apply the Law of Cosines The angle across from the largest side is the greatest angle. The largest angle is .

  9. Vocabulary Heron’s Area Formula:

  10. 4 EXAMPLE Write and Solve a real – Use trig to find area of triangle Jeju Traffic Triangle Find the area of the traffic triangle. 750 SOLUTION 1. Find the semi-perimeter s 2. Use Heron’s Area Formula: The area of the traffic triangle is .

  11. Lesson 9.6 Homework: • Practice B • Practice C “Honors”

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