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Math Help - Geometry picture problem

  1. #1
    Junior Member
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    Geometry picture problem

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    (click on the picture for zoom in)

    im trying to solve for theta

    all i see is the 30 60 90 triangle
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, john doe!

    We need more information.

    What is that quadrilateral on the hypotenuse . . . a square?
    Is that NE-SW slanted line through the center of the square?
    . . And is it parallel to the sides of the square?


    Assuming all that is true, we have this diagram:
    Code:
                            *
                           *   *
        A *               *       *
          |  *           *           *
          |     *       *      O        *
          |        *   *       *       *
          |           *       /|      *
          |              *   /θ|     *
          |                P*  |    *
          |                /  Q*   *
          |               /    |  *
          |                    |     *
          |                    |        *
          |                    |       30 *
          *  *  *  *  *  *  *  *  *  *  *  *  *
          C                    R              B

    We have right triangle ABC with \angle C = 90^o,\;\angle B = 30^o

    A square sits on hypotenuse AB; O is the center of the square.
    . .
    Actually, it could be any point in the square!

    OP \perp AB,\;\;OQR \perp CB


    In right triangle QRB,\;\angle B = 30^o \quad\Rightarrow\quad \angle BQR = 60^o

    Then \angle OQP = 60^o .
    (vertical angles)

    Therefore, in right triangle OPQ,\;\theta \:=\:\angle POQ \:=\:30^o

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  3. #3
    Junior Member
    Joined
    Aug 2008
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    What is that quadrilateral on the hypotenuse . . . a square?
    yea i think its a square it sure looks like one

    Is that NE-SW slanted line through the center of the square?
    yea the same it looks like its though the center

    And is it parallel to the sides of the square?
    i cant tell because there no indication that they are parallel


    How do you know angle C is 90 degrees?
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