The Pythagorean theorem is a fundamental principle used in geometry to find the length of a side of a right triangle. It states that for a right triangle with legs a and b, and hypotenuse c, the following equation holds:
c2 = a2 + b2
Given the two legs as:
- a = 8.2 miles
- b = 3.1 miles
Step 1: Square both values
a2 = 8.22 = 67.24
b2 = 3.12 = 9.61
Step 2: Add the squares
67.24 + 9.61 = 76.85
Step 3: Take the square root to find c
c = √76.85 ≈ 8.77 miles
Therefore, the length of side C (the hypotenuse) is approximately 8.77 miles.