Question

determining a tangent ratio
what is the value of tan(60°)?
$\frac{1}{2}$
$sqrt{3}$
$\frac{sqrt{3}}{2}$
$\frac{1}{sqrt{3}}$

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B = 60^{\circ}\), the side opposite to \(\angle B\) is \(AC\) and the side adjacent to \(\angle B\) is \(BC\).
We can also use the property of a \(30 - 60-90\) triangle. In a \(30 - 60 - 90\) triangle, if the side adjacent to the \(60^{\circ}\) angle (\(BC\)) is \(x\) (here \(x = 6\)), and the side opposite to the \(60^{\circ}\) angle (\(AC\)) is \(x\sqrt{3}\).

Step2: Calculate \(\tan(60^{\circ})\)

Using the formula \(\tan(60^{\circ})=\frac{AC}{BC}\). Since \(AC = 6\sqrt{3}\) and \(BC=6\), then \(\tan(60^{\circ})=\frac{6\sqrt{3}}{6}=\sqrt{3}\)

Answer:

\(\sqrt{3}\) (corresponds to the second option)