Intro and motivation
This is a general answer as how I would approach the problem at hand. Using the situation in the question as the use case. This way the answer is a bit more generally applicable.
Laying out a mass of shapes
Laying out a mass of shapes with precision is time consuming. The tools that can help you are the Blend tool, Transform again, Transform each, Align, Custom Brushes and Symbols.
After analysis of the case seems that Blend tool, Transform again and Custom Brushes may come into question. At first you should not discount any method.
Deconstruct the problem
One tool might not be enough. For example the lines that don't hit the bottom, and part of the shapes cut of by some invisible shape? Same applies to the other side.
Image 1: One possible deconstruction
An alternative view would be to think that there's no black lines but rather a solid black shape cut by white lines a top. The later view could make it easier to design equally spaced gaps.
In either any don't assume there's one tool that can solve the problem. You might need to cut shapes once you get the lines in right place. Or you might use multiple blends to make several parts of the fan shape, so one blend is right side of a line and the other is the left side.
Try many ways
Try several approaches until you get it, you might not succeed with the first try. And after trial you know better what the tools work and can make a better assumptions and trials.
And in the worst case scenario its still not a big job to draw them all manually with a line sued as a ruler stick moved about. Its just about 30 lines or 60 line sides if you need to manually do the stroke (you can merge them with no need to draw connecting segments). Which is not such a big deal in the grand scheme of things.