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anonymous

  • 5 years ago

If you have a triangle with angles of 30, 60 and 90 with a side of 12, what would the other two sides be?

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  1. amistre64
    • 5 years ago
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    which side is 12?

  2. amistre64
    • 5 years ago
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    side opposite 30 = 12? side opposite 60 = 12? or side opposite 90 = 12? these are 3 different results....

  3. anonymous
    • 5 years ago
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    oops I wrote it wrong, the side opposite is 21

  4. anonymous
    • 5 years ago
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    opposite 30

  5. anonymous
    • 5 years ago
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    you can use the law of of sines or cosines to get the answer

  6. anonymous
    • 5 years ago
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    law of sines is \[sineA/a=sinb/b\]

  7. anonymous
    • 5 years ago
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    \[Sin 30/21=sine 60/x\]

  8. anonymous
    • 5 years ago
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    cross multiply sin 30 x=(21)(sin60)

  9. anonymous
    • 5 years ago
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    Use a calculator to figure out the sines .05x = (21)(0.86602540378444) x=9.09326673973662

  10. anonymous
    • 5 years ago
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    so the side opposite 60 deg. is 9.09326673973662

  11. amistre64
    • 5 years ago
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    if you can visualize the 30-60-90 triangle (or draw it); then things get simpler as well; the slanted part(hypotenuse) has a normal value = 2 the leg opp. 60 has a normal value = sqrt(3) the leg opp. 30 has a normal value = 1 since opp 30 = 21 in your problem, then 1x = 21..x = 21 we want to multiply all these "normal" values by 21 to get the measurements of the other 2 sides: slant = 2(21) = 42 and leg opp 60 = 21sqrt(3) or 36.37

  12. anonymous
    • 5 years ago
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    I messed up in the last part of the algebra

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