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, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), the opposite side to \(60^{\circ}\) is \(x\) and the adjacent side is \(9\). So, \(\tan60^{\circ}=\frac{x}{9}\).

Step2: Substitute the value of \(\tan60^{\circ}\)

Since \(\tan60^{\circ}=\sqrt{3}\), we have \(\sqrt{3}=\frac{x}{9}\).

Step3: Solve for \(x\)

Multiply both sides by \(9\): \(x = 9\sqrt{3}\).

Answer:

\(x = 9\sqrt{3}\)