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.

2. How Does the Calculator Work?

The calculator uses the Pythagorean Theorem:

Where:

• \( a \) — Length of one side
• \( b \) — Length of the other side
• \( c \) — Length of the hypotenuse

Explanation: The theorem relates the lengths of all three sides of a right triangle, allowing you to calculate any side if you know the other two.

3. Importance of the Pythagorean Theorem

Details: This fundamental mathematical principle is essential in geometry, trigonometry, architecture, physics, engineering, and many practical applications involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of any two sides of a right triangle to calculate the third side. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this only work for right triangles?
A: Yes, the Pythagorean Theorem only applies to right-angled triangles.

Q2: What if I know the hypotenuse and one side?
A: You can rearrange the formula to calculate the unknown side: \( a = \sqrt{c² - b²} \).

Q3: What units should I use?
A: The calculator works with any consistent units (cm, m, inches, etc.) as long as both inputs use the same unit.

Q4: Can I use this for 3D space?
A: The theorem extends to 3D as \( d = \sqrt{a² + b² + c²} \) for calculating space diagonals.

Q5: What's the historical significance?
A: Known to ancient Babylonians and Egyptians, but Pythagoras is credited with the first formal proof.