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Math Help - A Triangle

  1. #1
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    A Triangle

    This question is related to a vector/force question, but I just need help with finding two angles:

    Given the following triangle:



    and knowing that a+b = 14. How can you figure out the length of a and b?
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by ty2391 View Post
    This question is related to a vector/force question, but I just need help with finding two angles:

    Given the following triangle:



    and knowing that a+b = 14. How can you figure out the length of a and b?
    Well I can clearly see a right angled triangle. So i think the answer is a = 8 and b = 6
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  3. #3
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    Sorry, the diagram may be misleading, im trying to say that the 6 and 4 split the top into two sections. (thanks for your reply though)

    Anyway, I figured it out I believe, can someone confirm that: a=54/7 and b=44/7?
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  4. #4
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    Quote Originally Posted by ty2391 View Post
    This question is related to a vector/force question, but I just need help with finding two angles:

    Given the following triangle:



    and knowing that a+b = 14. How can you figure out the length of a and b?
    Call the clearly vertical leg (that obviously is intended to meet the side of length 10 at a right angle) c.

    Then we know that
    a^2 = 6^2 + c^2 = 36 + c^2
    and
    b^2 = 4^2 + c^2 = 16 + c^2

    Then
    a^2 - b^2 = 20

    But
    a^2 - b^2 = (a + b)(a - b)
    and we know that a + b = 14. Thus
    14(a - b) = 20

    a - b = \frac{10}{7}

    Thus we have the system of equations
    a + b = 14

    a - b = \frac{10}{7}

    This has a solution of
    a = \frac{54}{7}
    and
    b = \frac{44}{7}

    (Which are at least close to Isomorphism's a = 8 and b = 6.)

    -Dan

    EDIT: Just saw your post ty2391. Obviously I agree with your answer. Good job.
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  5. #5
    Lord of certain Rings
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    Quote Originally Posted by ty2391 View Post
    Sorry, the diagram may be misleading, im trying to say that the 6 and 4 split the top into two sections. (thanks for your reply though)

    Anyway, I figured it out I believe, can someone confirm that: a=54/7 and b=44/7?
    Ya sorry... your answer is right

    Good job
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