Question

find w.

write your answer in simplest radical form.

boxed{} kilometers

Explanation:

Step1: Identify trigonometric ratio

We use cosine for angle $60^\circ$: $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=60^\circ$, adjacent side $=10$ km, hypotenuse $=w$.

Step2: Substitute values into ratio

$\cos60^\circ = \frac{10}{w}$
We know $\cos60^\circ = \frac{1}{2}$, so:
$\frac{1}{2} = \frac{10}{w}$

Step3: Solve for $w$

Cross-multiply: $w = 10 \times 2$

Answer:

20 kilometers