In this exercise, we have a triangle $ABC$ with a line $EF$ drawn parallel to $AC$. You are instructed to calculate the length of $AB$.

Here's a breakdown of the information we have:

1. Triangle $ABC$ with a line $EF \parallel AC$.
2. Some segment lengths are marked on the diagram:
   • $BE = 2.5$
   • $EF = 3.5$
   • $FG = 2.6$

Since $EF \parallel AC$, we can apply the properties of similar triangles. Typically, when a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. This means that the triangles $\triangle ABE$ and $\triangle ABC$ are similar.

To calculate $AB$, we would need to know the proportional relationship between $BE$ and $EF$, but it seems $AC$ itself or another measurement might be missing from the provided data. If any additional lengths or specific proportional information between the segments are provided, it would allow us to solve for $AB$ precisely.

Could you confirm if there are more measurements or details? If not, I can provide a general method to proceed.

Would you like further clarification on similar triangles or proportional relationships? Here are some additional questions that might extend this topic:

1. How does the similarity of triangles help in solving problems involving parallel lines?
2. What would change in the solution if $AC$ was given?
3. Could we use trigonometric ratios if more angles were provided?
4. What if $EF$ wasn’t parallel to $AC$? How would that affect the similarity?
5. How could we determine the scaling factor if only partial information is provided?

Tip: Remember, when lines are parallel in a triangle, corresponding sides of similar triangles maintain proportional lengths.