The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that:
a² + b² = c²
Here, c is the hypotenuse (the side opposite the right angle and the longest side), and a and b are the other two sides.
Given two sides of lengths 17 km and 15 km, we need to determine which side corresponds to which variable. Usually, if you want to find side B, then the other side and the hypotenuse must be known.
Case 1: Given sides a = 15 km and c = 17 km (hypotenuse), find b:
- Start with the formula: a² + b² = c²
- Substitute known values: 15² + b² = 17²
- Calculate squares: 225 + b² = 289
- Subtract 225 from both sides: b² = 289 - 225 = 64
- Take the square root: b = √64 = 8 km
Case 2: Given sides b = 15 km and a = 17 km, and you want to find the hypotenuse c:
- Use the formula: a² + b² = c²
- Calculate: 17² + 15² = c²
- Calculate squares: 289 + 225 = c²
- Sum: 514 = c²
- Find c: c = √514 ≈ 22.7 km
Summary: To solve for side B using the Pythagorean theorem, you need to know which sides correspond to the legs and hypotenuse. Then plug in the known values to solve for B.