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Math Help - Biggest possible area of triangle

  1. #1
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    Biggest possible area of triangle

    Given Three points with parameter "t" on the coordinate system

    A (cos(3-t) ; sin(3-t))
    B (cos(t) ; sin(t))
    C (-cos(t) ; -sin(t))

    for which meaning of "t" will the triangle ABC have the biggest area, if t (0;1)
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Biggest possible area of triangle

    You can see that all three points are 1 unit away from the origin, and that points B and C are always opposite each other with respect to the origin. So you can consider line BC as the base of the triangle with length 2. To make the area of the traingle a maximum you want the line OA to be at right angles to line BC (if you'd like a beter explanation as to why this is so post back). Consequently to maximimize the triangle area you want angle 3-t to be at right angles to angle t, or in other words either:

    3-t = t + pi/2
    or
    3-t = t-pi/2.

    Solve for t.
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  3. #3
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    Re: Biggest possible area of triangle

    Thanks for taking the time to discuss this, I feel strongly about it and love learning more on this topic. If possible, as you gain expertise, would you mind updating your blog with more information? It is extremely helpful for me.
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    Re: Biggest possible area of triangle

    Quote Originally Posted by waqas View Post
    Thanks for taking the time to discuss this, I feel strongly about it and love learning more on this topic. If possible, as you gain expertise, would you mind updating your blog with more information? It is extremely helpful for me.
    Which is his blog?
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  5. #5
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    Re: Biggest possible area of triangle

    Hi telo,
    ebaines has given you the answer. The following attachment arrives at the same answer in possibly a simpler way:

    Biggest possible area of triangle-mhfgeometry33.png
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