# Thread: One spot and distance known, Second spot unknown

1. ## 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?

2. ## 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.

3. ## 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: . $y \;=\;QP + RQ \;=\;L\sin\theta + r\cos\theta$