1. What is the Pythagorean Theorem?

Definition: 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.

Purpose: This fundamental relation helps calculate distances and lengths in right-angled triangles, with applications in construction, navigation, physics, and more.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: Enter any two sides to calculate the third side. The calculator automatically determines which side to calculate based on your input.

3. Importance of the Pythagorean Theorem

Details: This theorem is essential in geometry and has practical applications in construction, architecture, engineering, and computer graphics for calculating distances and angles.

4. Using the Calculator

Tips: Enter any two known sides (leave the third field empty) and click calculate. 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 units should I use?
A: Any consistent unit (meters, feet, inches, etc.) can be used as long as all sides use the same unit.

Q3: Can I calculate angles with this?
A: No, this only calculates side lengths. Use trigonometric functions (sine, cosine) for angles.

Q4: What if I get an error?
A: Make sure the hypotenuse is the longest side. If calculating legs, ensure the hypotenuse value is larger than the other leg.

Q5: How accurate are the results?
A: Results are mathematically precise, though displayed with 3 decimal places for readability.