Right Triangle X Y Z has a right angle labeled upper X. The side across from angle upper X is 34, the side across from angle upper Y is 30, and the side across from angle upper Z is 16.

Question

Question
Use the triangle to answer the question.
Find the sine of angle Y.
(1 point)
Responses

Start Fraction 8 over 15 End Fraction
Image with alt text: Start Fraction 8 over 15 End Fraction

Start Fraction 8 over 17 End Fraction
Image with alt text: Start Fraction 8 over 17 End Fraction

Start Fraction 17 over 15 End Fraction
Image with alt text: Start Fraction 17 over 15 End Fraction

Start Fraction 15 over 17 End Fraction
Image with alt text: Start Fraction 15 over 17 End Fraction

Answer 1

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