Extremlity,
Smart Guides being your friends (telling you when you are within snapping distance), a silly old way is to:
1) With the relevant (left) Handle visible (Direct Select the Anchor Point or the relevant (left) segment), ClickDrag with the Line Segment Tool from the Handle into the Anchor Point (that way because the Handle disappears);
2) Click the relevant Reference Point (in the case shown it is the top right) and multiply the W or H value by a suitable/ridiculous number (or set a value) and press Ctrl/Cmd+Enter to create a long (enough) guide line;
3) Direct Select the Anchor Point or the relevant (left) segment again, then ClickDrag the Handle as far as desired;
4) Delete the guide line from 2).