Question

find the sine of \\( \angle y \\).
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\( \sin ( y ) = \\)

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle Y\), the side opposite to \(\angle Y\) is \(WX = 30\), and the hypotenuse is \(WY=34\).

Step2: Calculate \(\sin(Y)\)

\(\sin(Y)=\frac{WX}{WY}\). Substitute \(WX = 30\) and \(WY = 34\) into the formula: \(\sin(Y)=\frac{30}{34}\). Then simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 30 and 34 is 2. So \(\frac{30\div2}{34\div2}=\frac{15}{17}\).

Answer:

\(\frac{15}{17}\)