Question

find n.

write your answer in simplest radical form.

miles

submit

Explanation:

Step1: Identify trigonometric ratio

We use tangent for the 60° angle: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, where $\theta=60^\circ$, opposite side is $n$, adjacent side is $5\sqrt{2}$.

Step2: Substitute values and solve for $n$

$\tan(60^\circ)=\sqrt{3}$, so:
$$n = 5\sqrt{2} \times \tan(60^\circ)$$
$$n = 5\sqrt{2} \times \sqrt{3}$$
$$n = 5\sqrt{6}$$

Answer:

$5\sqrt{6}$ miles