Question

find the exact value of \\( \sin c \\) in simplest radical form.
answer
attempt 1 out of 2
\\( \sin c= \\)

Explanation:

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

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(C\), the side opposite to angle \(C\) is \(AB = 5\), and the hypotenuse is \(AC=\sqrt{41}\).

Step2: Apply the formula

\(\sin C=\frac{AB}{AC}\)

Substitute \(AB = 5\) and \(AC=\sqrt{41}\) into the formula: \(\sin C=\frac{5}{\sqrt{41}}\)

Rationalize the denominator: \(\sin C=\frac{5\sqrt{41}}{41}\)

Answer:

\(\frac{5\sqrt{41}}{41}\)