1 / 25

As a matter of fact, right triangles end up being more of a rarity than commonplace.

There is no doubt that the 3 PTRs are extremely useful when solving problems modeled on a right triangle. Unfortunately, the world does not consist only of right triangles…. As a matter of fact, right triangles end up being more of a rarity than commonplace.

Download Presentation

As a matter of fact, right triangles end up being more of a rarity than commonplace.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. There is no doubt that the 3 PTRs are extremely useful when solving problems modeled on a right triangle. Unfortunately, the world does not consist only of right triangles…

  2. As a matter of fact, right triangles end up being more of a rarity than commonplace.

  3. There are many situations where angles other than 90O are present.

  4. Does that mean when we come across a situation that can only be modeled with a non-right triangle that we abandon our pursuit?….

  5. No Way!!!! There exists two Laws of Trigonometry that allow one to solve problems that involve non-right Triangles: The Law of Sines The Law of Cosines

  6. RememberA capital letter represents an angle in a triangle, and a small letter represents a side of a triangle a A

  7. The Law of Cosines

  8. (the blue line also forms a “c”, [kind of] which is how I remember to use the “c”osine law in this case..) If b,c and O are all known, then O is called a “Contained Angle” C a b O B A c

  9. The Cosine Law can be used to find the length of the opposite side to O In this case, the length of side a C a b O B A c

  10. In General: a2 = b2 + c2 – 2bcCosOo C a b O B A c

  11. For Example: Find a C a 8m 50o B A 10m

  12. a2 = b2 + c2 – 2(b)(c)CosAo a2 = 82 + 102 – 2(8)(10)Cos50o a2 = 61.15m You should be able to load this into your calculator directly from left to right…if not, see me a = 7.8 m C a 8m 50o B A 10m

  13. The Law of Sines

  14. The Sine Law If the triangle being solved does not consists of a right triangle (3PTRs) or a contained angle (Cosine Law), then another tool must be used.

  15. If a corresponding angle and side are known, they form an “opposing pair” A C b a O2 O1 B c

  16. The Sine Law can be used to determine an unknown side or angle given an “opposing pair” A C b a O2 O1 B c

  17. The Sine Law SinA = SinB = SinC a b c C a b A B c

  18. Find the length of a We can not use the Cosine Law because there is not a contained angle… We must therefore look for an opposite pair. Hmmm….. C a 57o A-HA!!! (it’s all good) c 73o N A 24

  19. Find the length of a C a = 24 a Sin73o Sin57o 57o a = 27.4 Again, this can be put directly into your calculator. See me for help. c 73o N A 24

  20. Pg 290 1a,c,d,e 4a,c,e 5a,c 6 8,10,12,14 Pg 295 1 (11 unco, stop here)

  21. The Ambiguous Case

  22. Find A 11 SinA Sin48o = 11 9 9 A = 65.3o Does that make sense? 48o A No Way!!!

  23. Side 9 can also be drawn as: Could A be 65o in this case? 11 9 48o A

  24. This type of discrepancy is called the “Ambiguous Case”Be sure to check the diagram to see which answer fits:O, or 180o - O

More Related