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 of the right triangle
• \( b \) — Length of the other side of the right triangle

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

3. Importance of Hypotenuse Calculation

Details: Calculating the hypotenuse is fundamental in geometry, architecture, navigation, and many engineering applications where right angles are involved.

4. Using the Calculator

Tips: Enter the lengths of both sides (a and b) in the same units. Both values must be positive numbers.

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: \( a = \sqrt{c² - b²} \)

Q3: What units should I use?
A: Any consistent units (cm, m, inches, etc.) as long as both sides use the same units.

Q4: Can this be used in 3D space?
A: Yes, the concept extends to 3D with \( d = \sqrt{x² + y² + z²} \)

Q5: How accurate is this calculation?
A: Mathematically exact for perfect right triangles. Real-world accuracy depends on measurement precision.