Comment 1 for bug 405835

A workaround that may work for you:

Assume the line you want to shorten is straight:

1: Turn on "Snap to paths" and turn off "Snap to grids" (or just hit # to deactivate grids)
2: Select Node tool
3: Select the node on the straight line you want to shorten

4: Keep Ctrl+Alt while dragging the node closer to the intersection point. By holding down Ctrl+Alt the node sort of snap to the lines original angle. Now you'll be able to put the node at the exact point on intersection.