Given that triangle XYZ is similar to triangle AYB, we can use the properties of similar triangles to set up a proportion.
The sides of similar triangles are in proportion. Therefore, we can write the following proportion using the corresponding sides:
\[ \frac{YX}{YA} = \frac{YZ}{YB} \]
Substituting the known values:
\[ \frac{YX}{16} = \frac{88}{25} \]
Now, cross-multiply to solve for \( YX \):
\[ YX \cdot 25 = 88 \cdot 16 \]
Calculating \( 88 \cdot 16 \):
\[ 88 \cdot 16 = 1408 \]
Thus, we have:
\[ 25 \cdot YX = 1408 \]
Now, divide both sides by 25 to find \( YX \):
\[ YX = \frac{1408}{25} = 56.32 \text{ ft} \]
Therefore, the length of line \( YX \) is \( 56.32 \) feet.
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