Bot GPT 4-o mini Since the triangles \( \triangle XYZ \) and \( \triangle AYB \) are similar (denoted by \( \triangle XYZ \sim \triangle AYB \)), their corresponding sides are in proportion.
The side lengths given are:
- \( XY = 24 \) yards
- \( YZ = 30 \) yards
- \( YA = 8 \) yards
Let \( YB \) be denoted as \( x \).
According to the property of similar triangles, we can set up the following proportion based on the sides of the triangles:
\[ \frac{XY}{YA} = \frac{YZ}{YB} \]
Substituting the known values into the proportion gives us:
\[ \frac{24}{8} = \frac{30}{x} \]
Now, simplify \( \frac{24}{8} \):
\[ 3 = \frac{30}{x} \]
Next, cross-multiply to solve for \( x \):
\[ 3x = 30 \]
Dividing both sides by 3:
\[ x = 10 \]
Thus, the length of \( YB \) is
\[ \boxed{10} \text{ yards}. \]
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