Question

10 multiple choice 1 point
find the value of the variable(s). if your answer is not an integer, leave it in
simplest radical form.
not drawn to scale
$\frac{1}{2}$
2
$9sqrt{3}$
$18sqrt{3}$

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), the adjacent side is \(9\), and the opposite side is \(t\). So, \(\tan60^{\circ}=\frac{t}{9}\).
Since \(\tan60^{\circ}=\sqrt{3}\), we have \(\sqrt{3}=\frac{t}{9}\).

Step2: Solve for \(t\)

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

Answer:

\(9\sqrt{3}\) (the third option)