Question

find the exact value of sin u in simplest radical form.

Explanation:

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

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

Step2: Identify the lengths of the sides

We are given that \(WV = \sqrt{17}\) and \(WU=9\).

Step3: Calculate \(\sin U\)

Using the formula \(\sin U=\frac{WV}{WU}\), substituting the values we get \(\sin U=\frac{\sqrt{17}}{9}\)

Answer:

\(\frac{\sqrt{17}}{9}\)