Corner of path tapering to a point

[tonyac55643645]

I'm trying to learn Illustrator so I'm sure this is a basic question, but I can't figure it out.  I have a curved path that abruptly changes direction at one point.  If angle of the corner that creates is large enough, the corner of the path tapers to a point like I want.  If it's ever so slightly smaller, the corner is blocky.  Please see animated gif:

Note how the path on the left has a nice point at the corner, and the path on the right looks chopped off.  Is there any way to get the path on the left to taper the same way?

[Monika Gause · Accepted solution]

In the strokes panel there is a value "Miter limit". Just use a higher value in there.

[Doug A Roberts]

In the stroke panel, increase the mitre limit until the point is visible.

With some corners, the mitre may be absurdly huge because of the angle the tangents of each path segment's stroke meets at:

[tonyac55643645]

Excellent, thank you both.  Not only does that fix it, it helps me understand why it's happening.