Given that triangle XYZ is similar to triangle AYB, we can use the properties of similar triangles to find the length of YX.
From the information provided, we have:
- \( YB = 15 , \text{ft} \)
- \( YA = 9 , \text{ft} \)
- \( YZ = 63 , \text{ft} \)
In similar triangles, the ratios of corresponding sides are equal. This allows us to set up a proportion based on the known lengths.
The sides from triangle AYB correspond to the sides from triangle XYZ as follows:
- \( YA \) corresponds to \( YZ \)
- \( YB \) corresponds to \( YX \)
Using the similarity ratio, we can set up the relationship:
\[ \frac{YA}{YZ} = \frac{YB}{YX} \]
Substituting the given values into the equation:
\[ \frac{9}{63} = \frac{15}{YX} \]
Now, simplify \( \frac{9}{63} \):
\[ \frac{9}{63} = \frac{1}{7} \]
Now the equation becomes:
\[ \frac{1}{7} = \frac{15}{YX} \]
Cross-multiplying gives:
\[ 1 \cdot YX = 15 \cdot 7 \]
Calculating the right side:
\[ YX = 105 \]
Thus, the length of \( YX \) is
\[ \boxed{105 , \text{ft}} \]