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Math Help - triangle

  1. #1
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    Question triangle

    Find the value of x, y, and z reduced to the simplest radical form. Please explain! Thank you in advance!
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  2. #2
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    Exclamation Diagram

    Ooops...forgot diagram...Here it is!
    Attached Thumbnails Attached Thumbnails triangle-xyz.jpg  
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by IHATECHONGAS View Post
    Ooops...forgot diagram...Here it is!
    ok, because i ws wondering what x, y, and z are you talking about?

    so by Pythagoras' theorem:
    x = sqrt(y^2 - 4^2) and also x = sqrt(z^2 - 2^2)

    => sqrt(y^2 - 4^2) = sqrt(z^2 - 2^2)
    => y^2 - 16 = z^2 - 4
    => y^2 - z^2 = 12 ..................(1)


    by Pythagoras' theorem:
    y = sqrt(6^2 - z^2) and also y = sqrt(x^2 + 4^2)
    => sqrt(6^2 - z^2) = sqrt(x^2 + 4^2)
    => 36 - z^2 = x^2 + 16
    => x^2 + z^2 = 20 ...................(2)


    by Pythagoras' theorem:
    z = sqrt(6^2 - y^2) and also z = sqrt(x^2 + 2^2)
    => sqrt(6^2 - y^2) = sqrt(x^2 + 2^2)
    => 36 - y^2 = x^2 + 4
    => x^2 + y^2 = 32 ....................(3)

    So we have the system:
    y^2 - z^2 = 12 ..................(1)
    x^2 + z^2 = 20 ..................(2)
    x^2 + y^2 = 32 ..................(3)

    solving this system should give you your values

    can you take it from here?
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