The Pythagorean theorem is a formula used in right-angled triangles to find the length of one side when the lengths of the other two sides are known. The formula is:
a² + b² = c²
where c is the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.
Given two sides of lengths 17 km and 15 km, you want to find side A. Depending on which side A represents (whether it's the hypotenuse or one of the legs), the approach changes:
Case 1: If 17 km and 15 km are the legs (a and b), and you want to find the hypotenuse (A = c)
Use the formula:
A = c = √(17² + 15²)
Calculating:
- 17² = 289
- 15² = 225
- Sum = 289 + 225 = 514
- Square root: √514 ≈ 22.68 km
Therefore, side A (the hypotenuse) is approximately 22.68 km.
Case 2: If 17 km is the hypotenuse (c) and 15 km is one leg (b), find the other leg A (a)
Use the rearranged formula to find a leg:
A = a = √(c² - b²) = √(17² - 15²)
Calculating:
- 17² = 289
- 15² = 225
- Difference = 289 - 225 = 64
- Square root: √64 = 8 km
Therefore, side A is 8 km.
Summary: Identify which sides correspond to legs or hypotenuse, then apply the Pythagorean theorem accordingly to solve for side A.