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First let me say I'm not an engineer, therefor my description might be a bit strange.
I'm building a program on request for some engineers and the idea is to create a pipe connection based on 2 sets of lines that cross eachother. Now I created this and it looked nice, however, they want the whole line to be measurable, so the cap of the secondary pipe needs to be calculated exactly. But no one can tell me how, so I'm hoping someone here knows.
This is how it looks now. How can I calculate the coordinates of the end point of the secondary pipe? The top of the cone.

Hope it's understandable and someone can help me with this. Thanks in advance!

This is a basic analytic geometery challenge. Most 3-D CAD programs can do this type of development quite easily.

How with the users input the information into the program?

Do you need the equations necessary or do you want it to be a graphical presentaion?

It has been years since I had to develop the necessary patterns. There are a number of places on the internet that may have what your are looking for - Search terms - intersection of pipes by analytical geometery

Niel Leon
engineering.com

It's based on MicroStation 2D. The input is basically 4 lines which need to be transformed into something like shown in the picture. They need to be able to measure the lines so it needs to be accurate with how the welders will build it in the end.