Merging two perpendicular curved surfaces and then cutting away part of one

So I’m trying to merge the cave like structure with the vertical wall. Both structures have curved surfaces. So I pushed the front edge of the cave till it stuck out from the vertical wall. Then I zoomed in on the intersecting edges and drew lines to define the surface that I want to cut away. (I.E. delete the front of the wall that closes off the cave) I made sure that the start and end points of each line are jumping to the intersection point (which isn’t easy). The problem I’m running in to is some of the lines no matter how much I zoom in and redraw them aren’t defining a solid shape as you can see in the image. This is allowing the surface I want to delete to extend past the line that should be confining it. Any tips on how to fix this would be greatly appreciated.

Select all faces that are involved and choose Intersect Faces with Selection.

Here’s an image of the front of the wall where you can see the dark lines that aren’t fully attached to the vertical surface and thus allowing the parts of the vertical surface to extend past the top edge of the cave opening. Which then means I can’t delete it.

Is that available in the web based free version?

Yes, make the selection then right click and it will be in the context menu.

Do I need to select the surfaces and the lines or just the surfaces?

Just make a right to left selection over the whole area.

Intersect Web

It worked Woohoo much thanks.

If the process of merging two curved shapes together caused one of the parts of the model to loose it’s surface does anyone know a way to fix it?

That is a rather broad question, sharing the model or at the very least a screenshot would help us answer.

Sorry my bad.

It is very difficult to tell from your screenshots, probably just need some stitching, but so many edges showing confuses things. Turn off back edges, keyboard shortcut k.
It would be easier to advise you if you download the model to your computer then attach it here.

Oh Hot dam thank you for the K tip. I’ve been trying to turn those off for months.

I’ve tried drawing lines from connecting points on the two lines and I can get a surface to form but it’s an ugly patchwork quilt.

Laser Tag Arena 2.skp (1.4 MB)
Here is a copy of the Sketchup file to look at.

I look forward to the answer - fixing missing patchwork faces

Use Line tool to create geometry (edges and faces), then smooth&soften them.