Question

solve for a. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary. draw show your work here hint: to add the square root symbol (√□), type
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Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), the opposite side to the \(60^{\circ}\) angle is \(a\), and the adjacent side is \(2\). So, \(\tan60^{\circ}=\frac{a}{2}\).
Since \(\tan60^{\circ}=\sqrt{3}\), we have the equation \(\sqrt{3}=\frac{a}{2}\).

Step2: Solve for \(a\)

Multiply both sides of the equation \(\sqrt{3}=\frac{a}{2}\) by \(2\) to isolate \(a\).
\(a = 2\sqrt{3}\).

Answer:

\(a = 2\sqrt{3}\)