Question

1. solve for $x$. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary.

Explanation:

Step1: Use the tangent function

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

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

We know that \(\tan60^{\circ}=\sqrt{3}\). Then the equation becomes \(\sqrt{3}=\frac{x}{9}\).

Step3: Solve for \(x\)

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

Answer:

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