To calculate the intersection of lines, 2 possible types of input are needed.
A. Two coordinates with both a bearing with respect to the North.
B. Four coordinates which form 2 line segments with an intersection.
Both methods can be used here to calculate the intersection. To use method A., enter point A with a bearing and point B with a bearing. To use methode B., all four coordinates need to be entered knowing that line segment one consists of point A and point B and line segment two consists of point C and point D.
The formula used is not always well defined for 'vertical' and 'horizontal' lines. Which means lines with a bearing of 0°, 360° or 180° and 90° or 270°. A very small adjustment in the coordinates will solve the problem. For small distances, which is common in geocaching , this error is neglectable.
Determining the intersection of lines can also be done on your GPS, handy when you are out on the trails.
Enter all waypoints in your GPS device (project waypoints with sufficient distance when only the bearing is known). Next go to the route screen of your GPS device and select the waypoints. Make sure you enter them in the correct order, the route needs to intersect with itself. If location A is top left, location D top right, location C bottom left and location B bottom right, a correcter order would be, A,B,C,D. Now view the route on the map, the route will intersect at the location you need to be. It will probably be handy to make a waypoint at the intersection for easy navigation. Make sure to do this while zooming in as far as possible to improve accuracy.