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.