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IloveCharlie

A triangular metal frame has sides 8 feet, 12 feet, and 16 feet. Find the measure of the largest angle between any two sides of the frame. The cosine of the largest angle=?

  • one year ago
  • one year ago

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  1. sasogeek
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    do you know the cosine rule?

    • one year ago
  2. IloveCharlie
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    Can you tell me it again? I forgot it

    • one year ago
  3. Nickv_1
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    adjacent over hypotenuse

    • one year ago
  4. IloveCharlie
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    Thanks @Nickv_1 So @sasogeek I just use that?

    • one year ago
  5. Nickv_1
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    welcome

    • one year ago
  6. sasogeek
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    we're not exactly sure if it's a right angled triangle, so we can't also conclude that it's adjacent over hypotenuse.... where is the adjacent, and where is the hypotenuse?

    • one year ago
  7. sasogeek
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    see, the cosine rule says that if you have a triangle, |dw:1344729963224:dw| \(\huge cosA=\frac{b^2+c^2-a^2}{2bc} \) we can substitute the values and solve for A (each angle) and see which one is the largest :) then we can find the cosine of that largest angle :)

    • one year ago
  8. sasogeek
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    let's say for example using this triangle, |dw:1344730155989:dw| \(\huge cosA=\frac{16^2+8^2-12^2}{2(16*8)} \) we can solve for A by taking the cos inverse of the value on the right side of the equation.

    • one year ago
  9. IloveCharlie
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    "on the right side of the equation"?

    • one year ago
  10. sasogeek
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    yeah, every equation has 2 sides :) left side = right side | | | | \(cosA \ \ \ \ = \frac{16^2+8^2-12^2}{2(16*8)} \)

    • one year ago
  11. sasogeek
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    so to find A, we find the cos inverse of the right side, like this... \(\huge A = cos^{-1}(\frac{16^2+8^2-12^2}{2(16*8)}) \)

    • one year ago
  12. sasogeek
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    are we good to go?

    • one year ago
  13. IloveCharlie
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    I'm trying to solve. Just a sec

    • one year ago
  14. sasogeek
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    sure :)

    • one year ago
  15. IloveCharlie
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    I keep getting error when trying to solve using my TI83

    • one year ago
  16. sasogeek
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    hmm, let's see what i get..just a sec

    • one year ago
  17. sasogeek
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    angle A = 79.193 degrees :)

    • one year ago
  18. IloveCharlie
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    Thank you! So the final answer is 79.193?

    • one year ago
  19. sasogeek
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    no, you'll have to check the other angles to be sure which one is the largest :)

    • one year ago
  20. IloveCharlie
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    Oh o.k. So I use the same formula?

    • one year ago
  21. sasogeek
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    yeah :) i'll do it and tell you what i got, in the mean time, do it yourself and let me know what you got too :)

    • one year ago
  22. IloveCharlie
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    Sounds good

    • one year ago
  23. IloveCharlie
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    :)

    • one year ago
  24. sasogeek
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    sorry i made a mistake somewhere, A=46.567 B=104.478 C=28.955

    • one year ago
  25. IloveCharlie
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    Oh :/ Was it the formula or a mistake in the arithmetic?

    • one year ago
  26. sasogeek
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    i just miscalculated, the formula is correct though, the last answers i put up are right... did u get the same thing?

    • one year ago
  27. IloveCharlie
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    Yes, I used the formula :) So obviously B is the largest angle

    • one year ago
  28. sasogeek
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    :) so u got the largest angle, what are u supposed to do with it?

    • one year ago
  29. IloveCharlie
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    Take cosine. So just a sec... -.2500?

    • one year ago
  30. sasogeek
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    yay! :) our work is done here :)

    • one year ago
  31. IloveCharlie
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    And I couldn't have done it without you! Thank you so much I really appreciate it :)

    • one year ago
  32. sasogeek
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    anytime :) you're welcome :)

    • one year ago
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