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anonymous

  • one year ago

An obtuse triangle has angle measurements of 100°, 60°, and 20°. If the longest side of this triangle is 20 feet, what is the length of its shortest side, s?

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  1. anonymous
    • one year ago
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  2. johnweldon1993
    • one year ago
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    Have you heard about the law of sines?

  3. anonymous
    • one year ago
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    yes @johnweldon1993

  4. johnweldon1993
    • one year ago
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    Cool because I didnt know how to go about this if you didnt lol Okay so we know \[\large \frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}\]

  5. anonymous
    • one year ago
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    lol okay @johnweldon1993

  6. johnweldon1993
    • one year ago
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    So we have the side of 20 ft....and the angle that faces it is 100 degrees right? And we have the angle that faces the 's' side that we want is the 20 degrees right?

  7. anonymous
    • one year ago
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    right. @johnweldon1993

  8. johnweldon1993
    • one year ago
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    So we can set up our law of sines to be \[\large \frac{sin(100)}{20} = \frac{sin(20)}{s}\] and solve for 's'

  9. anonymous
    • one year ago
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    okay i think i got it, for this problem i got 6.9 ft is that correct? @johnweldon1993

  10. johnweldon1993
    • one year ago
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    *shouldda calculated it huh* ...yeah 6.9 is correct :)

  11. anonymous
    • one year ago
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    okay thanks! :-) could you help me with another one? @johnweldone1993 please

  12. johnweldon1993
    • one year ago
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    Oh god another one????? >.< haha no jk of course :P

  13. anonymous
    • one year ago
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    haha thanks, okay so ABCD is a parallelogram. Its diagonal, AC, is 18 inches long and forms a 20° angle with the base of the parallelogram. Angle ABC is 130°. What is the length of the parallelogram’s base, AB?

  14. anonymous
    • one year ago
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    @johnweldon1993

  15. johnweldon1993
    • one year ago
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    Hint. what do all the angles in any triangle add up to?

  16. anonymous
    • one year ago
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    360?? @johnweldon1993

  17. johnweldon1993
    • one year ago
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    Not quite...that is a circle :) the interior angles of a triangle ALWAYS add up to 180 degrees okay? So here...focus on the lower triangle |dw:1432857360434:dw|

  18. johnweldon1993
    • one year ago
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    So to solve for that angle labeled ?? right now We know those 3 angles will add to make 180...so if we already have 20...and 130....what would the other angle be?

  19. anonymous
    • one year ago
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    OHHHHH. crap sorry for some reason i was thinking of a square. and yes so 30?? @johnweldon1993

  20. johnweldon1993
    • one year ago
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    Lol no problem :) and yes 30 good...so we have |dw:1432857553567:dw| now we just have the law of sines again :) we have the angle 30 facing that side we need and we have the angle 130 facing the 18 we have so \[\large \frac{sin(130)}{18} = \frac{sin(30)}{b}\] and solve for 'b'

  21. anonymous
    • one year ago
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    right. @johnweldon1993 and we cross multiply??

  22. johnweldon1993
    • one year ago
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    mmhmm just like last time :)

  23. anonymous
    • one year ago
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    so sin130(b)

  24. johnweldon1993
    • one year ago
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    So we have yes \[\large sin(130)b = 18sin(30)\] and solve for 'b'

  25. anonymous
    • one year ago
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    0.7660(b)=9.270? @johnweldon1993

  26. johnweldon1993
    • one year ago
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    Solving for 'b' would get?

  27. anonymous
    • one year ago
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    8.504? @johnweldon1993

  28. johnweldon1993
    • one year ago
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    Not quite, lets head back to the original equation after cross multiplying \[\large sin(130)b = 18sin(30)\] If you divide both sides by sin(130) we get \[\large \frac{\cancel{sin(130)}b}{\cancel{sin(130)}} = \frac{18sin(30)}{sin(130)}\] showing that \[\large b = ?\]

  29. anonymous
    • one year ago
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    12.10? @johnweldon1993

  30. johnweldon1993
    • one year ago
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    Hmm also not what I get....am I doing something wrong? Lol I get b = 11.75

  31. anonymous
    • one year ago
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    nope i probably did i probably plugged it in wrong in my calculator @johnweldon1993 but thanks so much for your help!

  32. johnweldon1993
    • one year ago
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    Just wanted to make sure and I got it again so I would say go with it :P not to say yours is wrong of course >.< lol but Anytime :)

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