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 (the legs).

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

• \( c \) — Hypotenuse (longest side)
• \( a \) — First leg of the triangle
• \( b \) — Second leg of the triangle

Explanation: The theorem relates the lengths of the sides of any right triangle, allowing calculation of any side when the other two are known.

3. Importance of Pythagorean Theorem

Details: This fundamental relation in Euclidean geometry is widely used in mathematics, physics, engineering, architecture, and many practical applications involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of both legs (sides a and b) in any consistent units. The calculator will compute the hypotenuse length in the same units.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all triangles?
A: No, only for right-angled triangles where one angle is exactly 90 degrees.

Q2: What if I know the hypotenuse and one leg?
A: You can rearrange the formula: \( a = \sqrt{c^2 - b^2} \) to find the missing leg.

Q3: What units should I use?
A: Any consistent length units (cm, m, inches, etc.) can be used as long as both inputs are in the same units.

Q4: Can this be used in 3D space?
A: Yes, the theorem extends to three dimensions with \( d = \sqrt{a^2 + b^2 + c^2} \).

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though practical measurements may have precision limitations.