Question

find the exact value of \\( \sin y \\) in simplest radical form.
answer
\\( \sin y = \\)

Explanation:

Step1: Recall the definition of sine in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle Y\), the side opposite to \(\angle Y\) is \(WX = 14\), and the hypotenuse is \(YW=16\).

Step2: Calculate \(\sin Y\)

Using the formula \(\sin Y=\frac{WX}{YW}\), substitute \(WX = 14\) and \(YW = 16\). So, \(\sin Y=\frac{14}{16}\). Simplify the fraction by dividing both the numerator and the denominator by 2. \(\sin Y=\frac{7}{8}\).

Answer:

\(\frac{7}{8}\)