Question

what is the exact value of the sine ratio using β as the reference angle?
type only the final answer in the box below.

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For angle $\beta$ (at vertex B), the opposite side to $\beta$ is AC (length 12), and the hypotenuse is AB (length 13).

Step2: Apply the formula

Using the definition, $\sin(\beta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{12}{13}$.

Answer:

$\frac{12}{13}$