The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse:
a² + b² = c²
where c is the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.
You mentioned sides of 8 miles and 6 miles and want to find side B. Here's how to approach the problem, step by step:
- Identify the sides: Determine which side is the hypotenuse and which sides are legs. Usually, the largest side length is the hypotenuse.
- If 8 miles and 6 miles are the legs (the sides adjacent to the right angle), then side B could be the hypotenuse.
- If one of the sides is the hypotenuse, and you want to find the other leg, then B is a leg.
Let's consider both cases:
Case 1: Find hypotenuse B if legs are 8 mi and 6 mi
The formula for hypotenuse is:
B = √(8² + 6²) = √(64 + 36) = √100 = 10 miles
Case 2: Find leg B if hypotenuse is 8 mi and other leg is 6 mi
The formula to find a leg is:
B = √(hypotenuse² - other_leg²) = √(8² - 6²) = √(64 - 36) = √28 ≈ 5.29 miles
Summary:
- If 8 mi and 6 mi are legs, then B (hypotenuse) = 10 mi.
- If 8 mi is hypotenuse, and 6 mi is leg, then B (other leg) ≈ 5.29 mi.
Make sure you know which side you want to find and whether you know if the given sides include the hypotenuse.