Question

find the length of side $x$ in simplest radical form with a rational denominator.
answer attempt 1 out of 2
$x =$

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, for an angle \(\theta = 30^{\circ}\), the side opposite to \(\theta\) is \(4\) and the side adjacent to \(\theta\) is \(x\). We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan30^{\circ}=\frac{4}{x}\).
Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have the equation \(\frac{1}{\sqrt{3}}=\frac{4}{x}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\frac{1}{\sqrt{3}}=\frac{4}{x}\) to get \(x = 4\sqrt{3}\).

Answer:

\(x = 4\sqrt{3}\)