The image shows a 45°-45°-90° right triangle with the hypotenuse labeled $9\sqrt{3}$ km and one leg labeled as $s$. In a 45°-45°-90° triangle, the relationship between the legs and the hypotenuse is given by:

$\text{Hypotenuse} = \text{Leg} \times \sqrt{2}$

In this case, the hypotenuse is $9\sqrt{3}$, so we can set up the equation:

$9\sqrt{3} = s \times \sqrt{2}$

Now, solve for $s$:

$s = \frac{9\sqrt{3}}{\sqrt{2}}$

To simplify this, multiply the numerator and denominator by $\sqrt{2}$ to rationalize the denominator:

$s = \frac{9\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{9\sqrt{6}}{2}$

Thus, the value of $s$ is:

$s = \frac{9\sqrt{6}}{2} \text{ km}$

This is the answer in simplest radical form.

Would you like further details or help with another question?

1. How is the relationship between the sides of a 45°-45°-90° triangle derived?
2. What are