Question

find g.

write your answer in simplest radical form.

millimeters

Explanation:

Step1: Identify triangle type and trigonometric relation

This is a right - triangle. We can use the tangent function. For the \(60^{\circ}\) angle, \(\tan(60^{\circ})=\frac{g}{7}\) (since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), here \(\theta = 60^{\circ}\), opposite side is \(g\) and adjacent side is \(7\) mm).

Step2: Recall the value of \(\tan(60^{\circ})\)

We know that \(\tan(60^{\circ})=\sqrt{3}\). So from \(\tan(60^{\circ})=\frac{g}{7}\), we can solve for \(g\) by multiplying both sides by \(7\).
\(g = 7\times\tan(60^{\circ})\)
Substitute \(\tan(60^{\circ})=\sqrt{3}\) into the equation:
\(g = 7\sqrt{3}\)

Answer:

\(7\sqrt{3}\)