The force of resistance of the latch varies. at the time the door touches the latch it is zero and when it is pushed fully back it is k*d.
Edit
why F*tan j is the horizontal component? after OP's comment.
If we draw the perpendicular, $F_d*cos j,$ and $F_d* Sin j \ , $ components of Fd on the surface of latch, the hypotenuse of the triangle is the tan of that angle and is the horizontal component factor of the Fd.
We have ignored the round corner of the door on the diagram and assumed it's a sharp point.
End of edit. $$ F_d*tanj=k*d \\F_d=\frac{k*d}{tanj }$$
The steeper the angle J the less force is needed to push the door open.