Question

find $t$.
write your answer in simplest radical form.
_____ yards

Explanation:

Step1: Identify trigonometric ratio

We use tangent for the 30° angle: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=30^\circ$, opposite side = $t$, adjacent side = $4\sqrt{3}$ yd.

Step2: Substitute values into formula

$\tan(30^\circ)=\frac{t}{4\sqrt{3}}$
We know $\tan(30^\circ)=\frac{1}{\sqrt{3}}$, so:
$\frac{1}{\sqrt{3}}=\frac{t}{4\sqrt{3}}$

Step3: Solve for $t$

Multiply both sides by $4\sqrt{3}$:
$t=\frac{1}{\sqrt{3}} \times 4\sqrt{3}$
Simplify: $t=4$

Answer:

4 yards