Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and...
Transcript of Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and...
![Page 1: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/1.jpg)
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
![Page 2: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/2.jpg)
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.
![Page 3: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/3.jpg)
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.
![Page 4: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/4.jpg)
Picture What do we know?
For what are we solving?
Law of Sines or Cosines?
![Page 5: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/5.jpg)
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?
![Page 6: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/6.jpg)
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?
![Page 7: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/7.jpg)
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?
![Page 8: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/8.jpg)
Using the Law of Sines and the Law of Cosines to Solve Triangles
10. Solve for f (in Law of Sines/Cosines packet)
![Page 9: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/9.jpg)
Using the Law of Sines and the Law of Cosines to Solve Triangles
11. Solve for AC (in Law of Sines/Cosines packet)
![Page 10: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/10.jpg)
12. From Law of Sines/Cosines Packet 23. From Review Packet
![Page 11: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/11.jpg)
#13 ‐ Solve for AB
![Page 12: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/12.jpg)
#14 ‐ Solve for BC
![Page 13: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/13.jpg)
#15 ‐ Solve for angle A
![Page 14: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/14.jpg)
#16 ‐ Solve for angle C
![Page 15: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/15.jpg)
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.
![Page 16: Law of Sines and Cosines - Appoquinimink High School of... · 2012-03-21 · Law of Sines and Cosines Why do I need them? To solve non‐right triangles. (We can use the Law of Sines](https://reader034.fdocuments.in/reader034/viewer/2022042606/5f9c94dced4866376228ee86/html5/thumbnails/16.jpg)
Homework:
In the Law of Sines and the Law of Cosines Packet:• 7 ‐ 9• 13 ‐ 16
In the review packet:• 22, 24, 25