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anonymous

  • 4 years ago

Law of Sines- The Ambiguous Case 1) m<C=29 degrees b=31 m c=27 m

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  1. anonymous
    • 4 years ago
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    |dw:1328495762650:dw|

  2. anonymous
    • 4 years ago
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    I have to find m<A

  3. anonymous
    • 4 years ago
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    I don't get how to start. :/

  4. anonymous
    • 4 years ago
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    lets find the big triangle first. by the law of sines you have \[\frac{\sin(29)}{27}=\frac{\sin(B)}{31}\] \[\frac{31\sin(29)}{27}=\sin(B)\] \[\sin(B)=.5566\] rounded so \[B=\sin^{-1}(.5566)=33.82\]

  5. anonymous
    • 4 years ago
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    |dw:1328496308131:dw|

  6. anonymous
    • 4 years ago
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    sorry for the lousy picture, but you can see you have two choices for angle A

  7. anonymous
    • 4 years ago
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    in big triangle angle A is 180-29-33.82 = 117.18

  8. anonymous
    • 4 years ago
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    That first response was great definitely helped! But what number would be the opposite & what number would be the adj? Cause that will help me determine the # of triangles.

  9. anonymous
    • 4 years ago
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    these are not right triangles so you do not have "opposite" and "adjacent"

  10. anonymous
    • 4 years ago
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    i was looking at the largter triangle first and using the laws of sines, because the invese sine funcion on your calculator will not give you the bigger angle, only the one less that 90 degrees

  11. anonymous
    • 4 years ago
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    My teacher gave us notes and it says if you have two sides & one opposite (NON-included) angle of a triangle then there are three possibilities:

  12. anonymous
    • 4 years ago
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    |dw:1328496610821:dw|

  13. anonymous
    • 4 years ago
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    How is this determined? opp \[\ge\] adj or opp \[\le\] adj

  14. anonymous
    • 4 years ago
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    that is the larger triangle, and first we solve for B because you have angle C, side c, and side b

  15. anonymous
    • 4 years ago
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    so you know three out of the 4 numbers for the ratio it is not a matter of "opposite" "adjacent" etc because these are not right triangles

  16. anonymous
    • 4 years ago
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    i labled them with the side c opposite angle C, side a opposite angle A and side b opposite angle B

  17. anonymous
    • 4 years ago
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    then you can use \[\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\][

  18. anonymous
    • 4 years ago
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    and since we know side c, angle C, side b we have three out of the 4 numbers for the ratio here \[\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\] allowing us to solve for angle B

  19. anonymous
    • 4 years ago
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    So the answer to find m<A is 117 degrees?

  20. anonymous
    • 4 years ago
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    the reason this is the "ambiguous case" is that there are two possible triangles, the ones i drew in the first picture. in the bigger triangle and A is 117.18

  21. anonymous
    • 4 years ago
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    *has angle A = 117.18

  22. anonymous
    • 4 years ago
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    the smaller triangle has a different angle, but that is now easy to find

  23. anonymous
    • 4 years ago
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    |dw:1328497019018:dw|

  24. anonymous
    • 4 years ago
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    Thank you so much! I got the hang of this now :)

  25. anonymous
    • 4 years ago
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    the other angle B, the one in the smaller triangle, has measure 180 - 33.82 = 146.18

  26. anonymous
    • 4 years ago
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    so the measure of angle A in the smaller triangle is \[180 - 29 - 146.18 = 4.82\]

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