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anonymous

  • 4 years ago

i need help solving a triangle with a Angle of 39.4 degrees there are 2 sides the longest side is 7.11 and a leg that is 3.56 i have to find the side opposite the 39.4 degree angle and the angles that correspond with the 2 sides

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  1. Hero
    • 4 years ago
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    You see that draw button? You should click that and try to create the triangle.

  2. anonymous
    • 4 years ago
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    |dw:1327274366132:dw| this is what it looks like

  3. Hero
    • 4 years ago
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    Apply law of Cosines

  4. anonymous
    • 4 years ago
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    which is \[\sqrt{b ^{2}+c ^{2}-ABcos(\theta)}\]right

  5. Hero
    • 4 years ago
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    Make sure it is right

  6. anonymous
    • 4 years ago
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    BCcos(theta)*** sorry

  7. anonymous
    • 4 years ago
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    no.. use a^2 = b^2 + c^2 - 2*b*c*cos(A)

  8. anonymous
    • 4 years ago
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    oh did i miss the 2?

  9. anonymous
    • 4 years ago
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    bingo x

  10. anonymous
    • 4 years ago
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    thats what is throwing me off

  11. anonymous
    • 4 years ago
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    thank you both

  12. phi
    • 4 years ago
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    and use the law of sines to find the angles.

  13. anonymous
    • 4 years ago
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    im convinced that im doing everything right but i cannot seem to get the right answer, i know this because i can not get the interior angles to equal 180 degrees

  14. phi
    • 4 years ago
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    what did you get for the 3rd side?

  15. anonymous
    • 4 years ago
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    4.91

  16. phi
    • 4 years ago
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    A to scale picture might help here |dw:1327279521199:dw|

  17. phi
    • 4 years ago
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    notice that the angle opposite 7.11 is quite large. Also, notice that sin A = x can have 2 answers symmetric about 90º (actually an infinite number of answers if we keep going... but only 2 within 180º)

  18. anonymous
    • 4 years ago
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    yes i see that

  19. phi
    • 4 years ago
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    so find the "other angle"

  20. phi
    • 4 years ago
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    if you found A find 90 + (90-A) = 180-A

  21. anonymous
    • 4 years ago
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    i used the law of sines and computed 7.11sin(39.4)/4.91 in my calculator but i took the inverse sin of the that

  22. phi
    • 4 years ago
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    and got?

  23. anonymous
    • 4 years ago
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    66.80

  24. anonymous
    • 4 years ago
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    and i repeated for the final angle and got 27.4

  25. phi
    • 4 years ago
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    but for the angle opposite side 7.11, 66.8 is too small. Find the *other angle* which is 180-A, or 180-66.8

  26. anonymous
    • 4 years ago
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    well that should be 78 degrees but im getting 27.4

  27. phi
    • 4 years ago
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    I am not being clear, am I? Your 39.4 and 27.4 are correct. the problem is your 66.8 is not correct. You did it right (take the inverse sin of 7.11sin(39.4)/4.91 but notice that there is another angle that has exactly the same sin (see picture up above) that angle is at 180-66.8

  28. anonymous
    • 4 years ago
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    ohhhhhhhh

  29. phi
    • 4 years ago
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    The only way to know which angle to choose is to notice that one of the angles is obtuse (greater than 90º) You found one way to notice... the angles did not add up to 180º so the culprit is the angle opposite the longest side, because that will be the largest angle

  30. anonymous
    • 4 years ago
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    okay ya that makes sense

  31. anonymous
    • 4 years ago
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    thank you so very much

  32. phi
    • 4 years ago
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    yw

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