Question

find j.
write your answer in simplest radical form.
yards

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
For the $30^\circ$ angle, opposite side is $j$, adjacent side is $5\sqrt{3}$ yd.
$\tan(30^\circ) = \frac{j}{5\sqrt{3}}$

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

$\tan(30^\circ) = \frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}} = \frac{j}{5\sqrt{3}}$

Step3: Solve for $j$

Multiply both sides by $5\sqrt{3}$:
$j = \frac{1}{\sqrt{3}} \times 5\sqrt{3}$
Simplify: $j = 5$

Answer:

5 yards