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Question

Feature
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
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 right triangle \( XYZ \), we can use the definition of sine in a right triangle. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle \( XYZ \):

• The side opposite angle \( Y \) is \( 30 \) (the side that is opposite angle \( Y \)).
• The hypotenuse is the side opposite the right angle (angle \( X \)), which is \( 34 \).

The sine of angle \( Y \) is calculated as:

\[ \sin(Y) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{30}{34} \]

This can be simplified:

\[ \sin(Y) = \frac{30 \div 2}{34 \div 2} = \frac{15}{17} \]

Thus, the sine of angle \( Y \) is:

\[ \sin(Y) = \frac{15}{17} \]

The correct response is:

Start Fraction 15 over 17 End Fraction.