The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (C) is equal to the sum of the squares of the other two sides (A and B):
C² = A² + B²
Here, we know:
- A = 8 km
- B = 5 km
Step 1: Square both sides A and B:
- A² = 8² = 64
- B² = 5² = 25
Step 2: Add the squares:
C² = 64 + 25 = 89
Step 3: Find the square root of both sides to solve for C:
C = √89 ≈ 9.43 km
Answer: The length of the hypotenuse C is approximately 9.43 kilometers.