Question

find the side labeled x

Explanation:

Step1: Identify the trigonometric ratio

Since we have a right - triangle, adjacent side \(a = 14\) and hypotenuse \(x\), and the angle \(\theta=30^{\circ}\). We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos30^{\circ}=\frac{14}{x}\).

Step2: Solve for \(x\)

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\). Then \(x=\frac{14}{\cos30^{\circ}}\). Substitute \(\cos30^{\circ}\) value: \(x = \frac{14}{0.866}\approx16.2\).

Answer:

\(16.2\)