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 calculator helps find the length of the hypotenuse when you know the lengths of the other two sides of a right triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The squares of both legs are added together, and the square root of this sum gives the hypotenuse length.

3. Practical Applications

Details: This calculation is essential in construction, navigation, computer graphics, and any field requiring spatial measurements.

4. Using the Calculator

Tips: Enter the lengths of both legs (sides a and b) in any consistent units (meters, feet, etc.). Both values must be > 0.

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 units should I use?
A: Any consistent linear units (meters, feet, inches), but both sides must use the same units.

Q3: What if I know the hypotenuse and one side?
A: Rearrange the formula to \( a = \sqrt{c^2 - b^2} \) to find the missing side.

Q4: How accurate is the result?
A: The calculator provides results to 3 decimal places for precision.

Q5: Can I use this for 3D space?
A: The formula extends to 3D as \( d = \sqrt{a^2 + b^2 + c^2} \) for spatial diagonals.