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Section 6.6 Law of Cosines

Chapter 6 – Trigonometric Functions: Right Triangle Approach. Section 6.6 Law of Cosines. Law of Cosines. Like the Law of Sines , the Law of Cosines is also used for oblique triangles. Law of Cosines. We have two possible cases for the law of cosines.

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Section 6.6 Law of Cosines

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  1. Chapter 6 – Trigonometric Functions: Right Triangle Approach Section 6.6 Law of Cosines 6.6 - Law of Cosines

  2. Law of Cosines • Like the Law of Sines, the Law of Cosines is also used for oblique triangles.

  3. Law of Cosines • We have two possible cases for the law of cosines. • Case 1 – Two sides and the included angle (SAS) • Case 2 – Three sides (SSS) 6.5 - Law of Sines

  4. Definition • Law of Cosines works when we have SAS or SSS.

  5. Hint for Solving SAS

  6. Solving Using SAS Solve the triangles shown below.

  7. Hint for Solving SSS

  8. Solving Using SSS Solve the triangle ABC if a = 8, b = 19, and c = 14.

  9. Application Two airplanes leave an airport at the same time on different runways. One flies directly north at 400 mph. The other flies on a bearing of N75E at 350 mph. How far apart will the airplanes be after two hours?

  10. Heron’s Formula

  11. Using Heron’s Formula Find the area of a triangle with a = 6 yards, b = 16 yards, and c = 18 yards.

  12. Example – pg. 481 • Find the area of the shaded figure, rounded to two decimals. 6.6 - Law of Cosines

  13. Examples – pg. 481 • Find the indicated side x or angle . (Use either the Law of Sines or Law of Cosines, as appropriate.) 6.6 - Law of Cosines

  14. More Examples – pg. 481 6.6 - Law of Cosines

  15. More Examples – pg. 482 6.6 - Law of Cosines

  16. More Examples – pg. 482 6.6 - Law of Cosines

  17. More Examples – pg. 482 6.6 - Law of Cosines

  18. More Examples – pg. 480 • Solve triangle ABC. 6.6 - Law of Cosines

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