To solve for $y$ in this similar triangle problem, we need to understand the relationship between the triangles. Since $\triangle ABC \sim \triangle XYZ$, we know that the corresponding sides are proportional.

The corresponding sides are:

• $AB$ corresponds to $XY$,
• $BC$ corresponds to $XZ$,
• $AC$ corresponds to $YZ$.

Given values:

• $AB = 34$, $AC = 16$, and $BC = 30$ for $\triangle ABC$,
• $XY = 15$ and $XZ = x$ for $\triangle XYZ$.

We can set up a proportion using the corresponding sides:

$\frac{AB}{XY} = \frac{BC}{XZ} = \frac{AC}{YZ}$

To find $YZ$ (which corresponds to $AC$), we use the proportion with $AC$ and $XY$:

$\frac{AB}{XY} = \frac{AC}{YZ}$

Substitute the known values:

$\frac{34}{15} = \frac{16}{YZ}$

Cross-multiply to solve for $YZ$:

$34 \cdot YZ = 16 \cdot 15$ $34 \cdot YZ = 240$ $YZ = \frac{240}{34} = 7.0588$

If you meant the hypotenuse length in