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Math Help - Another oldie

  1. #1
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    Another oldie


    A surveyor starts at the center of a circular park with radius 7 miles.

    He walks 3 miles directly east and drives a stake into the ground at point A.

    He walk directly north until he reaches the perimeter of the park.
    Then he walks directly west until he is directly north of the center,
    . . and drives a stake into the ground at point B.

    Find the distance \overline{AB}.


    [The shortest solution, please.]
    .
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  2. #2
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    here's the hint:

    diagonals of a rectangle are ... ?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Soroban View Post
    A surveyor starts at the center of a circular park with radius 7 miles.

    He walks 3 miles directly east and drives a stake into the ground at point A.

    He walk directly north until he reaches the perimeter of the park.
    Then he walks directly west until he is directly north of the center,
    . . and drives a stake into the ground at point B.

    Find the distance \overline{AB}.

    [The shortest solution, please.]
    .
    You have a rectangle one diagonal of which is a radius, AB is the other diagonal.

    CB
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  4. #4
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    Use pythagoras theorem, the shortest possible method, no need of trigonometry

    CLUE: IT IS A SURD!!!!
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  5. #5
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    Quote Originally Posted by ice_syncer View Post
    Use pythagoras theorem, the shortest possible method, no need of trigonometry

    CLUE: IT IS A SURD!!!!
    don't think so ...
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  6. #6
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    Quote Originally Posted by skeeter View Post
    don't think so ...
    no, use pythagoras theorem.
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  7. #7
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    let me guess! 7 miles may be?
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  8. #8
    Member Greengoblin's Avatar
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    ^^The diagonals of a rectangle are equal, so it equals the radius, 7 miles.
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  9. #9
    Super Member Aryth's Avatar
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    I know this is a while afterwards but, the solution is quite simple.

    One diagonal is a radius, so the Northern leg of the trip must be:

    3^2 + b^2 = 7^2

    b = \sqrt{40}

    So, the parallel side is also \sqrt{40}, so therefore the diagonal AB must be:

    3^2 + (\sqrt{40})^2 = c^2

    7 = c

    And there you go.

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  10. #10
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    You don't need to do that calculation. The two diagonals of a rectangle are of the same length and one of them is a radius. Since the circle is given as having radius 7 mi., the length of AB is 7 mi.
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