Hint 1:

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How many lines can I make if I have 1 coin? What if I have 2 coins?

Hint 2:

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How many coins do I have left I made the first line of the triangle?(Considering it could be made) Now how many coins do I need to make the second line? Under what condition can I make the second line.

Hint 3:

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Extending this idea, suppose we have already made i lines of the triangle.(Considering they could be made) How many coins are left with me? How many coins are needed to make the next line? Do I have enough coins left?

Hint 4:

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So can I construct a triangle starting from line 1. If the first line can be made, I can update the number of coins left. Next I try to make the second line. Now I require 2 coins for the second line. If I have 2 or more coins left with me, I can make the second line. And this process goes on.

Hint 5:

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When will this process end?