The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (usually labeled c) is equal to the sum of the squares of the other two sides (a and b):
c² = a² + b²
Here, you have two sides: 9 miles and 6 miles, and you want to find side A. First, determine whether the 9mi and 6mi are the legs (a and b) or if one of them is the hypotenuse (c).
Assuming 9 miles and 6 miles are the two legs of the right triangle, then side A would be the hypotenuse (c).
Step 1: Write down the formula:
c² = a² + b²
Step 2: Substitute the known values:
c² = 9² + 6² = 81 + 36 = 117
Step 3: Solve for c:
c = √117 ≈ 10.82 miles
Therefore, side A (the hypotenuse) is approximately 10.82 miles.
Alternative: If one of the sides, say 9 miles, is the hypotenuse (c), and 6 miles is one leg (a), and you are trying to find the other leg (b, which is side A), then:
Step 1: Use the formula b² = c² - a²
Step 2: Substitute values: b² = 9² - 6² = 81 - 36 = 45
Step 3: b = √45 ≈ 6.71 miles
So in that case, side A would be approximately 6.71 miles.
Make sure you correctly identify which sides are legs and which is the hypotenuse before applying the theorem.