question\nfind the length of side $x$ in simplest radical form with a rational denominator.\nanswer attempt…

Explanation:

Step1: Identify trigonometric ratio

We use tangent, since we have the opposite side to the 60° angle (length 9) and we need the adjacent side (x). The tangent of an angle in a right triangle is (\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}). (\tan(60^\circ) = \frac{9}{x})

Step2: Substitute (\tan(60^\circ)) value

We know (\tan(60^\circ) = \sqrt{3}). (\sqrt{3} = \frac{9}{x})

Step3: Solve for (x)

Rearrange the equation to isolate (x), then rationalize the denominator. (x = \frac{9}{\sqrt{3}} = \frac{9\sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{9\sqrt{3}}{3})

Step4: Simplify the expression

Divide the numerator by the constant denominator. (x = 3\sqrt{3})

Answer:

(3\sqrt{3})