Given the triangles \( \triangle XYZ \sim \triangle AYB \), we can use the property of similarity which states that the ratios of corresponding sides of similar triangles are equal.
From the problem, we have the following side lengths:
- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards
Let \( YB = x \). Since the triangles are similar, we can write the following proportion based on the corresponding sides:
\[ \frac{XY}{AY} = \frac{YZ}{YB} \]
Substituting the known lengths into the equation, we have:
\[ \frac{24}{8} = \frac{30}{x} \]
Simplifying the left side:
\[ 3 = \frac{30}{x} \]
Now, to solve for \( x \), we can cross-multiply:
\[ 3x = 30 \]
Dividing both sides by 3 gives:
\[ x = 10 \]
Thus, the length of \( YB \) is 10 yards. Therefore, the correct answer is:
10 yards.
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