You can try using the Align utility to achieve this.
1. Select both the circle and the triangle (with the

tool, click on one shape and then shift + click on the other)
2. Open the Align Panel (Shift + Ctrl + A or Object -> Align and Distribute)
3. Set the Align Relative to Selection from the drop down-list at the top-right corner of the Align Panel
4. Now center the two objects on the vertical (Its on the first row, third item from the left, looks like two arrows pointing at each other) and horizontal axis (second row, 3rd item from the left)
5. Now, select only the triangle, and move it upwards while holding the Ctrl key. You will have to judge with your eyes and place the triangle so it seems like it is on the tangent. Try zooming in with

tool for a closer look.
6. Now, you can join both objects to make one shape by selecting both and going to Path -> Union (You might have to do "Path -> Object to Path" first, but I think inkscape will automatically do this when told to make a Union)
7. With the

tool, select the newly formed shape and select one of the two nodes that "join" the triangle outline with the circle (you'll notice that they have the shape of a diamond). Then, look in the tool option at the top and you'll see an icon resembling a semi-circle with a square in the middle (it should say "make selected node smooth" when mouse is hovered above it). Click on the icon and then do the same to the other node on the other side of the shape. This should clear up any roughness that might have been there.
If something funky happens while smoothing the nodes, then that probably means inkscape created two nodes very close to each other while performing the union. Just delete one of them and it should stop messing up.