Given that triangles \( \triangle XYZ \sim \triangle AYB \), we can use the property of similar triangles that states the ratios of corresponding sides are equal.
Let's denote the lengths of the sides:
- \( XY = 24 \) yards (corresponds to \( YA \))
- \( YZ = 30 \) yards (corresponds to \( YB \))
- \( YA = 8 \) yards (corresponds to \( YB \))
From the similarity of the triangles, we can set up the ratio:
\[ \frac{XY}{YA} = \frac{YZ}{YB} \]
Substituting the known values:
\[ \frac{24}{8} = \frac{30}{YB} \]
Calculating \( \frac{24}{8} \):
\[ 3 = \frac{30}{YB} \]
Now, we can cross-multiply to solve for \( YB \):
\[ 3YB = 30 \]
Dividing both sides by 3:
\[ YB = 10 \text{ yards} \]
Thus, the length of \( YB \) is \( 10 \) yards. The correct response is:
10 yards.