The image shows two triangles, $\triangle ABC$ and $\triangle ATS$, where $\triangle ATS$ is similar to $\triangle ABC$. Given that $AS = 4$, and we are solving for $AC$, we rely on the properties of similar triangles.

Key Observations:

1. $\triangle ATS \sim \triangle ABC$ (indicated by the equal angles and proportional sides).
2. $AC$ includes both segments $AS$ and $SC$.
3. The proportionality of sides holds:

$\frac{AS}{AC} = \frac{TS}{BC}.$

Analysis:

• $AS = 4$: This is given.
• $TS$ and $BC$ are marked with similar proportions.
• Using similarity, $AC = 8$ because $AC$ is double $AS$ due to the given proportionality.

Answer:

$\boxed{8}$

Let me know if you'd like a deeper breakdown!

Related Questions:

1. How do you calculate the ratio of two similar triangles?
2. What other geometric properties are shared by similar triangles?
3. How would you determine the scale factor between two triangles?
4. If $TS$ was halved, how would it affect $AC$?
5. Can you apply the Pythagorean theorem to verify side lengths here?

Tip:

Always look for parallel sides and equal angles as clues for similar triangles!