Question

solve for ( x ). do not convert your answer to decimal form.
draw
show your work here
hint: to add the square root symbol (( sqrt{square} )), type
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Explanation:

Step1: Identify trigonometric ratio

In a right triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^\circ\), opposite side is \(x\), adjacent side is \(12\). So \(\tan(60^\circ)=\frac{x}{12}\).

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

We know that \(\tan(60^\circ)=\sqrt{3}\). Substitute into the equation: \(\sqrt{3}=\frac{x}{12}\).

Step3: Solve for \(x\)

Multiply both sides by \(12\): \(x = 12\sqrt{3}\).

Answer:

\(12\sqrt{3}\)