Question

given right triangle rst, what is the value of sin(s)? \\(\frac{5}{13}\\) \\(\frac{5}{12}\\) \\(\frac{12}{13}\\) \\(\frac{13}{12}\\)

Explanation:

Step1: Recall sine definition for angles

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle S$

Opposite side to $\angle S$ is $RT = 5$, hypotenuse is $ST = 13$

Step3: Calculate $\sin(S)$

$\sin(S) = \frac{5}{13}$

Answer:

$\frac{5}{13}$ (Option A)