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BloomLocke367

  • one year ago

Use the Law of Sines. Find m<C to the nearest tenth.

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  1. BloomLocke367
    • one year ago
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    |dw:1432755865708:dw|

  2. sparrow2
    • one year ago
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    m<c?

  3. BloomLocke367
    • one year ago
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    yes, the measure of angle C.

  4. BloomLocke367
    • one year ago
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    @Nnesha @perl @Preetha

  5. sparrow2
    • one year ago
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    so we need ti find sin24

  6. BloomLocke367
    • one year ago
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    but it's not a right triangle.

  7. BloomLocke367
    • one year ago
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    does that still apply?

  8. BloomLocke367
    • one year ago
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    I don't understand the Law of Sines

  9. sparrow2
    • one year ago
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    yes it still apply just write sin24

  10. BloomLocke367
    • one year ago
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    okay

  11. BloomLocke367
    • one year ago
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    I got 0.4067....

  12. BloomLocke367
    • one year ago
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    @sparrow2

  13. sparrow2
    • one year ago
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    so just enter this in the formula and then round nearest tenth

  14. BloomLocke367
    • one year ago
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    what formula?

  15. BloomLocke367
    • one year ago
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    @perl

  16. sparrow2
    • one year ago
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    law of sines

  17. BloomLocke367
    • one year ago
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    I don't know the formula.

  18. sparrow2
    • one year ago
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    162/sinc=77/sin24

  19. sparrow2
    • one year ago
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    then find sinc and look at the table to the relevant angle

  20. BloomLocke367
    • one year ago
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    what table? and I'm very confused right now..

  21. sparrow2
    • one year ago
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    values of trig function at different angle

  22. perl
    • one year ago
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    Does it make sense up to here $$ \Large \frac{\sin 24^o}{77}= \frac{\sin C}{162} $$

  23. BloomLocke367
    • one year ago
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    why is it like that?

  24. perl
    • one year ago
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    here is a diagram of the law of sines http://www.mathworksheetsgo.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/images/picture-law-of-sines-formula.jpg

  25. BloomLocke367
    • one year ago
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    ohhhh, yes that makes sense.

  26. perl
    • one year ago
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    so we are using just two parts of the three part ratio

  27. perl
    • one year ago
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    you can do that since they are equal

  28. BloomLocke367
    • one year ago
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    okay.

  29. perl
    • one year ago
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    we don't know `sin B` and `b` anyway at this point , yet

  30. BloomLocke367
    • one year ago
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    and we have to solve for C?

  31. perl
    • one year ago
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    $$ \Large{ \frac{\sin 24^o}{77}= \frac{\sin C}{162} \\~\\ \iff \\~\\ \sin 24^o \times 162 = 77 \times \sin C \\~\\ \iff \\~\\ \frac{\sin 24^o \times 162}{77} = \sin C }$$

  32. BloomLocke367
    • one year ago
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    okay. and how do we isolate C?

  33. perl
    • one year ago
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    $$ \Large{ \frac{\sin 24^o}{77}= \frac{\sin C}{162} \\~\\ \iff \\~\\ \sin 24^o \times 162 = 77 \times \sin C \\~\\ \iff \\~\\ \frac{\sin 24^o \times 162}{77} = \sin C \\~\\ \iff \\~\\ \sin^{-1} \left( \frac{\sin 24^o \times 162}{77} \right)= C }$$

  34. BloomLocke367
    • one year ago
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    that's what I thought, okay.

  35. perl
    • one year ago
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    make sure you are in degree mode if you are using a TI 83/84/85 calculator

  36. BloomLocke367
    • one year ago
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    I got 58.8

  37. BloomLocke367
    • one year ago
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    is that right?

  38. perl
    • one year ago
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    yes :)

  39. perl
    • one year ago
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    |dw:1432757526103:dw|

  40. BloomLocke367
    • one year ago
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    Oh, wow. Thank you so much! I might need your help later, but I don't know. \(\Huge\rlap{\tt\color{teal}{Thank~you!}}{\;\tt\color{lime}{Thank~you!}}\)

  41. perl
    • one year ago
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    Now try to 'solve' the triangle (find all side lengths and angles). You can find angle B using the fact that three angles of any triangle add up to 180. Then use law of sines one more time to find side b, or alternatively you can use law of cosines

  42. perl
    • one year ago
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    Your welcome :)

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