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 in Euclidean geometry helps calculate distances and solve problems involving right triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Hypotenuse (longest side opposite the right angle)
• \( a \) — One leg of the triangle
• \( b \) — Other leg of the triangle

Explanation: The calculator takes the lengths of two sides and computes the third side using the square root of the sum of squares.

3. Importance of the Pythagorean Theorem

Details: This theorem is essential in construction, navigation, physics, computer graphics, and many other fields where distance calculations are needed.

4. Using the Calculator

Tips: Enter any two sides of a right triangle to find the third side. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator find any side of the triangle?
A: Yes, you can rearrange the formula to solve for any side: \( a = \sqrt{c² - b²} \) or \( b = \sqrt{c² - a²} \).

Q2: Does this only work for right triangles?
A: Yes, the Pythagorean theorem applies exclusively to right-angled triangles.

Q3: What units should I use?
A: The calculator uses meters by default, but any consistent unit of length will work (feet, inches, etc.).

Q4: How accurate are the results?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.

Q5: Can I use this for 3D space?
A: The theorem extends to 3D as \( d² = a² + b² + c² \) for calculating space diagonals.