As it is a "cut" question, you can use knife project :
- In object mode select the "wall" part RMB
- Then both select the "floor" part Shift+RMB
- Enter edit mode Tab
- Place the view to the top ortho NumPad7
- Then use knife project in the tool panel
- Last step : remove the unwanted vertex
Knife project uses a mesh to cut into another. The cuts are given through the view plane (so it depends on from where you are looking). The cuts are given using the cutting object edges (from this point of view), to create new vertices and edges in the cut mesh.
A step further... this make an ngon (a face with more than 4 vertices) and it is better to avoid ngons...
First approach :
- Enter edit mode
- Select all and Ctrl+T to triangulate
- Then selecting quad parts Alt+J
Second approach :
- Remove the ngon face
- Subdivide the wanted edges W then subdivide
- Place the 3D cursor at the 'pivot vertex'
- Set pivot mode on 3D cursor
- Then move (scale) the vertices to the 3D cursor
- Last : remake the faces F and eventually correct the normals Ctrl+N
Other possible approaches, certainly...