The Pythagorean theorem is a fundamental principle used in geometry to find the length of a side in a right triangle. It states:
a² + b² = c²
Here, c represents the hypotenuse (the longest side opposite the right angle), and a and b are the other two sides.
Given two sides measuring 5 inches and 3 inches, and you want to find side A, you need to know whether side A is one of the legs or the hypotenuse.
Case 1: If 5 in and 3 in are the legs and you want to find the hypotenuse (A)
Use the formula:
A² = 5² + 3²
A² = 25 + 9 = 34
Take the square root of both sides:
A = √34 ≈ 5.83 inches
Case 2: If 5 in is the hypotenuse and 3 in is a leg, and you want to find the other leg (A)
Use the formula:
A² + 3² = 5²
A² = 25 - 9 = 16
Take the square root of both sides:
A = √16 = 4 inches
Summary: Depending on which side A represents, apply the Pythagorean theorem accordingly:
- If A is the hypotenuse, A = √(5² + 3²)
- If A is a leg, A = √(hypotenuse² - other leg²)