How to Use the Pythagorean Theorem to Find the Hypotenuse When Legs Are 3 miles and 1 mile

The Pythagorean theorem is a fundamental relation in geometry that applies to right triangles. It states that:

a² + b² = c²

where a and b are the lengths of the two legs (shorter sides) of the right triangle and c is the length of the hypotenuse (the side opposite the right angle).

Step-by-Step Solution:

1. Identify the sides: The two legs are 3 miles and 1 mile.
2. Write the formula: Using the Pythagorean theorem formula, a² + b² = c², plug in the values:
3. 
4. Calculate squares of legs:
• 3 miles squared: 3² = 9
• 1 mile squared: 1² = 1
5. Sum of squares: 9 + 1 = 10
6. Solve for c: To get c, take the square root of 10:
7. c = √10 ≈ 3.16 miles

Final answer: The length of the hypotenuse c is approximately 3.16 miles.