Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), the opposite side to \(60^{\circ}\) is \(x\) and the adjacent side is \(6\). So, \(\tan60^{\circ}=\frac{x}{6}\).
Since \(\tan60^{\circ}=\sqrt{3}\), we have the equation \(\sqrt{3}=\frac{x}{6}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sqrt{3}=\frac{x}{6}\) by \(6\).
\(x = 6\sqrt{3}\)

Answer:

\(x = 6\sqrt{3}\)