Question

2025 geometry e wwa right triangle relationships and trigonometry 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 $\sin(S)$ in right - triangle $RST$, the side opposite to angle $S$ is $RT$ and the hypotenuse is $ST$.

Step2: Identify side lengths

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

Step3: Calculate $\sin(S)$

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

Answer:

$\frac{5}{13}$