Question

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

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle W\), the side opposite to \(\angle W\) is \(XV = 24\), and the hypotenuse is \(XW=26\).

Step2: Calculate \(\sin(W)\)

\(\sin(W)=\frac{XV}{XW}\)
Substitute \(XV = 24\) and \(XW = 26\) into the formula: \(\sin(W)=\frac{24}{26}\)
Simplify the fraction \(\frac{24}{26}=\frac{12}{13}\) (divide both the numerator and the denominator by 2).

Answer:

\(\frac{12}{13}\)