Question

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

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to \(\angle F\)

For \(\angle F\), the opposite side is \(EG = 12\) and the hypotenuse is \(EF=13\).

Step3: Calculate \(\sin(F)\)

Using the formula \(\sin(F)=\frac{EG}{EF}\), we substitute \(EG = 12\) and \(EF = 13\). So, \(\sin(F)=\frac{12}{13}\).

Answer:

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