Question

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

Explanation:

Step1: Recall sine - function definition

The sine of an angle in a right - triangle is defined as $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle S$ in right - triangle $RST$, the side opposite to $\angle S$ is $RT$ and the hypotenuse is $ST$.

Step2: Identify the lengths

We are given that $RT = 5$ and $ST=13$.

Step3: Calculate $\sin(S)$

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

Answer:

$\frac{5}{13}$