Question

express sin q as a fraction in simplest terms.

Explanation:

Step1: Recall SOHCAHTOA for sine

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for angle Q

For angle \( Q \), the opposite side to \( Q \) is \( OP = 12 \), and the hypotenuse is \( OQ = 13 \).

Step3: Calculate \(\sin Q\)

Using the sine formula, \(\sin Q = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{OP}{OQ} = \frac{12}{13}\).

Answer:

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