# One spot and distance known, Second spot unknown

• Apr 10th 2012, 09:49 AM
cesar2012
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?
Attachment 23556
• Apr 10th 2012, 10:10 AM
biffboy
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.
• Apr 10th 2012, 11:01 AM
Soroban
Re: One spot and distance known, Second spot unknown
Hello,cesar2012!

Quote:

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