1. What is the Pythagorean Theorem?

Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Purpose: This fundamental relation helps calculate unknown lengths in right triangles, essential in geometry, construction, and physics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) and \( b \) — The two perpendicular sides (legs)
• \( c \) — The hypotenuse (side opposite the right angle)

Explanation: Enter any two known sides to calculate the third unknown side.

3. Practical Applications

Details: Used in construction for ensuring square corners, in navigation for calculating distances, and in various engineering calculations.

4. Using the Calculator

Tips:

• Enter any two known side lengths
• Leave the field you want to calculate as zero or empty
• All values must be positive numbers

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use?
A: The calculator works with any consistent units (meters, feet, etc.), just ensure all sides use the same unit.

Q3: What if I get an error?
A: Ensure the hypotenuse is the longest side. If calculating a leg, the hypotenuse must be longer than the other leg.

Q4: Can I use this for 3D calculations?
A: The basic theorem is for 2D, but there's a 3D extension: d² = a² + b² + c².

Q5: How accurate are the results?
A: The calculator provides precise mathematical results, but real-world measurements may have practical tolerances.