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The numbers 1-9 sum to 45. If they are to be sum to 15 on each of three sides of a triangle, no number can be counted more than once (15*3 = 45).
That is, there are no numbers at any of the vertices.
Then there are several possible options:
1, 5, 9 along one side,
2, 6, 7 along the second
3, 4, 8 along the third.
So, if x marks the vertices
. . . . .x
. . . .1 . 2
. . .5 . . . 6
. . 9 . . . . . 7
. x . 3 4 8 . x
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