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Understanding the Law of Sines and Cosines in Triangle Problems

In this lesson, students will learn how to convert degrees to radians and vice versa, focusing on angles like 30° and 240°. They will explore the Law of Sines and the Law of Cosines, understanding their definitions and applications. By the end of this lesson, students will be able to apply these laws to solve various triangle problems, including calculating areas. This foundational knowledge is crucial in trigonometry and geometric problem-solving.

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Understanding the Law of Sines and Cosines in Triangle Problems

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Presentation Transcript

  1. Warm-Up 5/29/13 Convert each degree to a radian and each radian to a degree 30° 240° 4.

  2. 13-4 Law of Sines

  3. CA Standard SWBAT: Know the law of sines and the law of cosines and apply those laws to solve problems.
  4. Area of a Triangle The area of a triangle is ½ the product of the lengths of two sides and the sine of their included angle. C A= ½bc sin A b a A = ½ac sin B A B A = ½ab sin C c
  5. Example 1: A = ½ ac sin B A = ½(5)(6) sin 112° A ≈ 13.9 Find the area of ABC to the nearest tenth. A 6 ft B 112° C 5 ft
  6. Example 2: Your Turn Find the area of ABC to the nearest tenth if A = 31°, b = 18 m, and c = 22m A = ½ bc sin A A = ½(18)(22) sin 31° A ≈ 102.0 m2
  7. Law of Sines Let ABC be any triangle with a, b, and c representing the measures if sides opposite angles with measurements A, B, and C respectively. Then
  8. Example 3: Solve ABC C b 55° a A 45° B 12
  9. Example 3: Solve ABC C b 55° 10.4 A 45° 80° 12
  10. Example 4: Your Turn Solve ABC C 17 20 A 118° B
  11. Example 4: Your Turn Solve ABC C 17 20 A 118° 49°
  12. Example 5: Your Turn Solve ABC C 12 13 A 25° B
  13. Example 5: Your Turn Solve ABC C 17 20 A 118° 49°
  14. Example 6: Your Turn Solve ABC C 9 5 A 50° B
  15. Your Homework pg. 790 #11-22
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