Question

and simplify your answer if necessary. draw 30° 13 w

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse is \(13\), and the side opposite to the \(30^{\circ}\) angle is \(w\).

Step2: Apply the sine formula

We know that \(\sin30^{\circ}=\frac{w}{13}\). Since \(\sin30^{\circ}=\frac{1}{2}\), we have the equation \(\frac{1}{2}=\frac{w}{13}\).

Step3: Solve for \(w\)

Cross - multiply the equation \(\frac{1}{2}=\frac{w}{13}\). We get \(w=\frac{13\times1}{2}\).

Answer:

\(w = 6.5\)