Question

given right triangle rst, what is the value of sin(s)?
options:

• \\(\frac{5}{13}\\)
• \\(\frac{5}{12}\\)
• \\(\frac{12}{13}\\)
• \\(\frac{13}{12}\\)

(image shows right triangle rst with right angle at r, rs = 12, rt = 5, st = 13)

Explanation:

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

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

Step2: Identify the lengths of the sides

We are given that \(RT = 5\) and \(ST=13\).

Step3: Calculate \(\sin(S)\)

Using the formula \(\sin(S)=\frac{RT}{ST}\), substituting \(RT = 5\) and \(ST = 13\), we get \(\sin(S)=\frac{5}{13}\).

Answer:

\(\frac{5}{13}\) (corresponds to the first option)