Question

find w.
triangle with 30°, 60°, right angle, 39 mi side
write your answer in simplest radical form.
blank miles

Explanation:

Step1: Identify trigonometric ratio

We use tangent, since we have the angle, adjacent side $w$, and opposite side 39 mi. The tangent of $30^\circ$ is $\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(30^\circ) = \frac{39}{w}$

Step2: Substitute $\tan(30^\circ)$ value

We know $\tan(30^\circ) = \frac{1}{\sqrt{3}}$.
$\frac{1}{\sqrt{3}} = \frac{39}{w}$

Step3: Solve for $w$

Cross-multiply to isolate $w$.
$w = 39\sqrt{3}$

Answer:

$39\sqrt{3}$ miles