This problem involves a right triangle, and the length of the hypotenuse $c$ can be calculated using the Pythagorean theorem:

$c^2 = a^2 + b^2$

Here:

• $a = 4$ miles
• $b = 2$ miles

Step 1: Substitute the values into the formula

$c^2 = 4^2 + 2^2$ $c^2 = 16 + 4$ $c^2 = 20$

Step 2: Solve for $c$ by taking the square root

$c = \sqrt{20}$

Step 3: Simplify and round to the nearest tenth

$c = \sqrt{20} \approx 4.47$

Rounded to the nearest tenth: $c \approx 4.5 \, \text{miles}$

Final Answer:

$c = 4.5 \, \text{miles}$

Let me know if you'd like a detailed breakdown of the steps!

Related Questions:

1. How can you determine the side lengths of a right triangle using trigonometry?
2. What is the relationship between the Pythagorean theorem and distance in geometry?
3. If the triangle’s sides were doubled, what would the new hypotenuse length be?
4. How would the answer change if the side lengths were given in kilometers instead of miles?
5. What is the significance of rounding to the nearest tenth in practical applications?

Tip:

When solving for square roots manually, remember that $\sqrt{20}$ can also be written as $2\sqrt{5}$, which may be helpful in simplifying expressions!