Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines and the Law of Cosines to solve any triangle.) Law of Sines: Law of Cosines: c 2 =a 2 +b 2 ‐ 2ab cos C b 2 =a 2 +c 2 ‐ 2ac cos B a 2 =b 2 +c 2 ‐ 2bc cos A
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Law of Sines and CosinesWhy do I need them? To solve non‐right triangles. (We can use the Law of Sines and the Law of Cosines to solve any triangle.)
Law of Sines:
Law of Cosines:
c2 = a2 + b2 ‐ 2ab cos Cb2 = a2 + c2 ‐ 2ac cos Ba2 = b2 + c2 ‐ 2bc cos A
How do I know which one to use!?!?
Law of Sines is best if:
Case 1: You know TWO sides, an angle opposite one of those sides, AND you're trying to find an angle opposite the other given side.
Case 2: You know two angles, one side, AND you're trying to find a missing side.
How do I know which one to use!?!?
Law of Cosines is best if:
Case 1: You know the length of all THREE sides AND you're trying to find an angle.
Case 2: You know TWO sides, the angle in between them, AND you're trying to find the side opposite the angle.
Picture What do we know?
For what are we solving?
Law of Sines or Cosines?
Using the Law of Sines and the Law of Cosines to Solve Triangles
16. Solve for AC (in review packet) Law of Sines or Cosines?
Using the Law of Sines and the Law of Cosines to Solve Triangles
18. Solve for BC (in review packet) Law of Sines or Cosines?
In review packet!
17. Law of Sines or Cosines? 19. Law of Sines or Cosines?
20. Law of Sines or Cosines? 21. Law of Sines or Cosines?
Using the Law of Sines and the Law of Cosines to Solve Triangles
10. Solve for f (in Law of Sines/Cosines packet)
Using the Law of Sines and the Law of Cosines to Solve Triangles
11. Solve for AC (in Law of Sines/Cosines packet)
12. From Law of Sines/Cosines Packet 23. From Review Packet
#13 ‐ Solve for AB
#14 ‐ Solve for BC
#15 ‐ Solve for angle A
#16 ‐ Solve for angle C
Exit Ticket
1. While sitting on the bench during a football game against Illinois, Rob Bolden decided to start his math homework. After looking at the triangle on the right, Rob determined that he could use the Law of Sines to solve for AB. Is he right? Why or why not?
2. Solve for AB.
Homework:
In the Law of Sines and the Law of Cosines Packet:• 7 ‐ 9• 13 ‐ 16
In the review packet:• 22, 24, 25
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