Question

in \\( \delta xyz \\), the measure of \\( \angle z = 90 ^ { \circ }, zy = 8, yx = 17 \\), and \\( xz = 15 \\). what is the value of the sine of \\( \angle y \\) to the nearest hundredth?

Explanation:

Step1: Recall the sine function definition

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

Step2: Substitute the values

We know that \(XZ = 15\) and \(YX=17\). So, \(\sin Y=\frac{XZ}{YX}\).
Substitute \(XZ = 15\) and \(YX = 17\) into the formula: \(\sin Y=\frac{15}{17}\).

Step3: Calculate the value

\(\frac{15}{17}\approx0.88\) (rounded to the nearest hundredth).

Answer:

\(0.88\)