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 (the legs).

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

• \( c \) — Hypotenuse (length units)
• \( a \) — First leg (length units)
• \( b \) — Second leg (length units)

Explanation: The theorem applies to all right-angled triangles, allowing calculation of any side if the other two are known.

3. Importance of Pythagorean Theorem

Details: Fundamental to geometry, used in construction, navigation, physics, computer graphics, and many practical applications involving right angles.

4. Using the Calculator

Tips: Enter lengths of both legs in any consistent units (meters, feet, etc.). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for non-right triangles?
A: No, the Pythagorean theorem only applies to right-angled triangles. For other triangles, use the Law of Cosines.

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

Q3: Does it matter which leg is a and which is b?
A: No, the theorem is symmetric with respect to the two legs.

Q4: Can I use this for 3D space?
A: Yes, the 3D extension is \( d = \sqrt{a^2 + b^2 + c^2} \) for spatial diagonals.

Q5: What's the historical significance?
A: Known to ancient civilizations, but Pythagoras is credited with the first formal proof. One of the most important mathematical discoveries.