The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (usually side C) is equal to the sum of the squares of the other two sides (A and B):
C² = A² + B²
From your question, you have two sides: 45 miles and 36 miles, and you want to find side B. Let's assume:
- A = 36 mi
- B = unknown side
- C = 45 mi
This setup suggests that 45 miles is the hypotenuse.
Using the theorem:
C² = A² + B²
Substitute the known values:
45² = 36² + B²
Calculate the squares:
2025 = 1296 + B²
Subtract 1296 from both sides:
2025 - 1296 = B²
729 = B²
Take the square root of both sides to find B:
B = √729 = 27
Therefore, side B is 27 miles long.