Question

find g.
3√2 mm
write your answer in simplest radical form.
millimeters

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function, since we know an angle, the adjacent side to the angle, and need the opposite side. For the 60° angle:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 60^\circ$, adjacent side = $g$, opposite side = $3\sqrt{2}$ mm.

Step2: Substitute values and solve for $g$

Rearrange the ratio to isolate $g$:
$g = \frac{3\sqrt{2}}{\tan(60^\circ)}$
We know $\tan(60^\circ) = \sqrt{3}$, so substitute:
$g = \frac{3\sqrt{2}}{\sqrt{3}}$

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{3}$:
$g = \frac{3\sqrt{2} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{3\sqrt{6}}{3}$

Step4: Simplify the expression

Cancel the common factor of 3:
$g = \sqrt{6}$

Answer:

$\sqrt{6}$ millimeters