Using the Pythagorean Theorem to Find the Hypotenuse C with Legs 8 mi and 5 mi

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

a² + b² = c²

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

Given:

• a = 8 miles
• b = 5 miles

We need to find c.

Step 1: Square both legs

Calculate the squares of both sides:

• 8² = 64
• 5² = 25

Step 2: Add the squares

Sum them up:

64 + 25 = 89

Step 3: Calculate the square root

The hypotenuse c is the square root of this sum:

c = √89

Using a calculator:

c ≈ 9.43 miles

Final answer:

The length of the hypotenuse C is approximately 9.43 miles.