This is related to some product design work I am doing and not being particular competent at maths have struggled to work out necessary steps in this problem. In summary, the problem is this. Two straight poles (P1 and P2) of length L1 and L2 are stuck in the ground a distance D apart (along the ground). P1 is at angle A1 to the vertical and P2 is at an angle A2 to the vertical. Two further poles (P3 and P4) are attached to P1 and P2. Pole P3 attaches at the bottom of P1 and attaches to the top of P2. Pole P4 attaches to the top of P1 and attaches to the bottom of P2. Poles P3 and P4 therefore cross each other at some point along their lengths. I simply wish to understand the basic steps in calculation I need to take to calculate the lengths of poles P3 and P4 and additionally the point at which they cross each other in terms of the point on pole P3 and the point on pole P4 that they cross. I thought this would be a straight forward problem to solve - it is easy to draw and therefore solve the problem diagrammatically - but I need to change values and therefore drawing is not feasible.

I would be grateful for any help. Basic steps in the calculations needed would be great. I can then plug these into a spreadsheet!

Many thanks for any time people can spend on this.

Regards

Luke