Give this a try...
Select the Bezier tool (Shift + F6) then look for the Bezier Mode on the taskbar, and select spiro path.
It'll probably be easier if you turn on Snapping and enable "Snap cusp nodes incl. rectangle corners"
With the bezier tool, snap onto the top edge of your shape. Then click a couple more times before snapping onto the bottom edge. After clicking at the bottom, hit return. You should have a line that looks something like what is shown in the pic below.
Press F2 to get the node tool and click the black line once. This will display the nodes on the line. Drag the mouse over the two nodes in the middle to highlight them. Note, do NOT highlight the end nodes!
Now, on the main taskbar, click the button that says "Make selected nodes smooth" and this will start to imitate a smooth curve.
Move the nodes around slightly if the angle looks slightly off or not quite smooth.
Finally, drag the mouse over both lines to select, then on the Path menu, click Union. This will unify your two lines into one object.
Here's a pic showing the instructions in greater detail.