Question

in \\( delta def \\), the measure of \\( angle f = 90 ^ { circ } \\), \\( ed = 53 \\), \\( df = 45 \\), and \\( fe = 28 \\). what ratio represents the sine of \\( angle d \\)?

Explanation:

Step1: Recall the sine formula

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

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

For \(\angle D\), the opposite side is \(FE\) and the hypotenuse is \(ED\).
Given \(FE = 28\) and \(ED=53\).

Step3: Calculate the sine of \(\angle D\)

\(\sin D=\frac{FE}{ED}\)

Answer:

\(\frac{28}{53}\)