1. What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This fundamental relation in Euclidean geometry is among the most famous mathematical theorems.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

• \( c \) — Hypotenuse (longest side)
• \( a \) and \( b \) — Other two sides (legs)

Explanation: The theorem applies to all right-angled triangles, relating the lengths of all three sides in a precise mathematical relationship.

3. Importance of the Theorem

Details: The Pythagorean Theorem is essential in geometry, trigonometry, architecture, navigation, and many STEM fields. It's used for calculating distances, designing structures, and solving real-world problems involving right angles.

4. Using the Calculator

Tips: Enter lengths of any two sides (a and b) in the same units. Values must be positive numbers. The calculator will compute the hypotenuse (c).

5. Frequently Asked Questions (FAQ)

Q1: Does this work for any triangle?
A: No, only for right-angled triangles where one angle is exactly 90 degrees.

Q2: What if I know the hypotenuse and one side?
A: You can rearrange the formula to find the missing side: \( a = \sqrt{c^2 - b^2} \).

Q3: What units should I use?
A: Any consistent length units (cm, m, inches, etc.), just ensure both inputs use the same units.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, though practical accuracy depends on your input measurements.

Q5: Can this be used in 3D space?
A: Yes, the theorem extends to 3D as \( d = \sqrt{x^2 + y^2 + z^2} \) for calculating spatial diagonals.