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Math Help - One spot and distance known, Second spot unknown

  1. #1
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    Question One spot and distance known, Second spot unknown

    Hi there, I know the coordinates of points E and Q, so I know their euclidean distance L.
    I'm looking for the point W with coordinates (a,b) related to other known values?
    One spot and distance known, Second spot unknown-geometry1.jpg
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  2. #2
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    Re: One spot and distance known, Second spot unknown

    Draw a line through Q parallel to the y-axis and add further to the diagram so that you have 2 right angled triangles. Then use trigonometry to get the other 2 sides in each triangle.
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  3. #3
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    Re: One spot and distance known, Second spot unknown

    Hello,cesar2012!

    I know the coordinates of points E and Q, so I know their euclidean distance L.
    I'm looking for the point W with coordinates (a,b) related to other known values.
    Code:
                            * * *
                      W o-----o R   *
                      *  *    |       *
                     *    *   |        *
                          r* @|
                    *        *|         *
                    *         o Q       *
                    *       * |         *
                          *   |
                     *  *     |        *
                  L   *       |       *
                    *   *     |     *
                  *         * * *
                *             |
              * @             |
          E o-----------------o P

    Note that: . \angle W\!QR \,=\,\angle QEP \,=\,\theta


    In \Delta QPE\!:\;\begin{Bmatrix}EP &=& L\cos\theta \\ QP &=& L\sin\theta \end{Bmatrix}

    In \Delta W\!RQ\!:\;\begin{Bmatrix}W\!R &=& r\sin\theta \\ RQ &=& r\cos\theta \end{Bmatrix}


    The x-coordinate of point W is: . x \;=\;EP - W\!R \;=\;L\cos\theta - r\sin\theta

    The y-coordinate of point W is: . y \;=\;QP + RQ \;=\;L\sin\theta + r\cos\theta
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