Question

do not convert your answer to decimal form. rationalize tfy your answer if necessary. draw 30° 13 w

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the adjacent side is \(13\), and the opposite side is \(w\). So, \(\tan30^{\circ}=\frac{w}{13}\).

Step2: Solve for \(w\)

Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(\frac{1}{\sqrt{3}}=\frac{w}{13}\). Cross - multiply to get \(w=\frac{13}{\sqrt{3}}\).

Step3: Rationalize the denominator

Multiply numerator and denominator by \(\sqrt{3}\), \(w=\frac{13\sqrt{3}}{3}\).

Answer:

\(w = \frac{13\sqrt{3}}{3}\)