Below are the command prompts to draw a polyline with a line, arc, and line where the last line segment is tangent to the curve.  The part highlighted in Red shows where you enter L to get back to a line mode from arc mode during command execution.  Enter L again to choose the Length option at the prompt for “next point”.  At the Specify length of line: prompt either type the length at the command line or pick two points on screen.  Only the length will be applied in the direction of the outgoing tangent of the arc to draw the next line segment.
Command: pl PLINE
Specify start point:
Current line-width is 0.000
Specify next point or [Arc/Halfwidth/Length/Undo/Width]:
Specify next point or [Arc/Close/Halfwidth/Length/Undo/Width]: a
Specify endpoint of arc or
[Angle/CEnter/CLose/Direction/Halfwidth/Line/Radius/Second pt/Undo/Width]:
Specify endpoint of arc or
[Angle/CEnter/CLose/Direction/Halfwidth/Line/Radius/Second pt/Undo/Width]: L
Specify next point or [Arc/Close/Halfwidth/Length/Undo/Width]: L
Specify length of line: <type a distance or pick a length>
Specify next point or [Arc/Close/Halfwidth/Length/Undo/Width]: