Question

find k. write your answer in simplest radical form. kilometers

Explanation:

Step1: Identify trigonometric ratio

We use cosine for the 60° angle: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=60^\circ$, adjacent side $=\sqrt{3}$ km, hypotenuse $=k$.

Step2: Substitute values and solve for k

Substitute into the ratio:
$\cos(60^\circ) = \frac{\sqrt{3}}{k}$
We know $\cos(60^\circ)=\frac{1}{2}$, so:
$\frac{1}{2} = \frac{\sqrt{3}}{k}$
Rearrange to solve for $k$:
$k = 2\sqrt{3}$

Answer:

$2\sqrt{3}$ kilometers