Question

find n. write your answer in simplest radical form. inches

Explanation:

Step1: Recall trigonometric ratio

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the hypotenuse is $4\sqrt{3}$ inches and the side opposite to the $30^{\circ}$ angle is $n$.

Step2: Apply the sine formula

We know that $\sin30^{\circ}=\frac{n}{4\sqrt{3}}$. Since $\sin30^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{n}{4\sqrt{3}}$.

Step3: Solve for $n$

Cross - multiply: $n=\frac{4\sqrt{3}}{2}$.

Step4: Simplify the result

$n = 2\sqrt{3}$ inches.

Answer:

$2\sqrt{3}$ inches