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:

• \( leg1 \) — Length of first leg
• \( leg2 \) — Length of second leg
• \( hypot \) — Length of hypotenuse

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

3. Importance of Right Triangle Calculations

Details: These calculations are fundamental in geometry, architecture, engineering, physics, and many practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter lengths of both legs in any consistent units. The calculator will return the hypotenuse in the same units. All 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: You can rearrange the formula to calculate the unknown leg: \( leg = \sqrt{hypot^2 - other\_leg^2} \).

Q3: What units should I use?
A: Any consistent units can be used (cm, inches, meters, etc.). The result will be in the same units as your input.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact. Any limitations would come from measurement precision of the input values.

Q5: Can I use this for 3D space calculations?
A: The theorem extends to 3D as \( d = \sqrt{x^2 + y^2 + z^2} \) for distance from origin to point (x,y,z).