Given that triangles \( \triangle XYZ \sim \triangle AYB \), we can use the properties of similar triangles which state that the corresponding sides are proportional.
The ratios of the sides can be set up as follows:
\[ \frac{XY}{AY} = \frac{YZ}{YB} \]
Now, we know the lengths:
- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards
Let \( YB \) be \( x \). Therefore, we can set up the proportions:
\[ \frac{24}{8} = \frac{30}{x} \]
Now, simplifying the left side:
\[ \frac{24}{8} = 3 \]
So, we have:
\[ 3 = \frac{30}{x} \]
Cross-multiplying gives us:
\[ 3x = 30 \]
Now dividing both sides by 3:
\[ x = 10 \]
Thus, the length of \( YB \) is \( 10 \) yards.
The correct answer is:
10 yards.