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. This relationship is fundamental in geometry.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem formula:

Where:

• \( a \) — Length of one side of the right triangle
• \( b \) — Length of the other side of the right triangle
• \( c \) — Length of the hypotenuse

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

3. Applications of the Pythagorean Theorem

Details: The theorem is used in various fields including architecture, engineering, physics, computer graphics, navigation, and more. It's essential for calculating distances and designing structures.

4. Using the Calculator

Tips: Enter the lengths of two sides of a right triangle to calculate the third side. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Can I calculate any side of the triangle?
A: This calculator finds the hypotenuse given the other two sides. To find a different side, rearrange the formula.

Q3: What units should I use?
A: Any consistent units can be used (cm, m, inches, etc.), just ensure both inputs use the same units.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though results are rounded to 4 decimal places for display.

Q5: Can this be used in 3D space?
A: The theorem extends to 3D as \( d = \sqrt{x^2 + y^2 + z^2} \) for calculating spatial distances.