Question

find n.
write your answer in simplest radical form.

yards

Explanation:

Step1: Identify triangle type & angles

This is a right triangle (90°, 60°, 30°). Use Law of Sines: $\frac{n}{\sin(90^\circ)} = \frac{8\sqrt{6}}{\sin(60^\circ)}$

Step2: Substitute sine values

$\sin(90^\circ)=1$, $\sin(60^\circ)=\frac{\sqrt{3}}{2}$. So $n = \frac{8\sqrt{6}}{\frac{\sqrt{3}}{2}}$

Step3: Simplify the expression

$n = 8\sqrt{6} \times \frac{2}{\sqrt{3}} = 16\sqrt{\frac{6}{3}} = 16\sqrt{2}$

Answer:

$16\sqrt{2}$ yards