To find the sine of angle \( Y \) in the right triangle \( XYZ \), we can use the sine ratio, which is defined as:
\[ \sin(Y) = \frac{\text{opposite side to angle Y}}{\text{hypotenuse}} \]
From the triangle data given:
- The side opposite angle \( Y \) (which is side \( XZ \)) is 30.
- The hypotenuse (which is the side across from the right angle, side \( YZ \)) is 34.
Now we can substitute these values into the sine formula:
\[ \sin(Y) = \frac{30}{34} \]
We can simplify this fraction:
\[ \sin(Y) = \frac{30 \div 2}{34 \div 2} = \frac{15}{17} \]
Therefore, the sine of angle \( Y \) is
\[ \sin(Y) = \frac{15}{17} \]
The correct response is:
Start Fraction 15 over 17 End Fraction