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 fundamental relation in Euclidean geometry is among the most well-known mathematical theorems.

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 applies to all right-angled triangles, allowing calculation of any side when the other two are known.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are essential in various fields including architecture, engineering, physics, and computer graphics. They form the basis for trigonometry and many practical measurement applications.

4. Using the Calculator

Tips: Enter the lengths of both legs (a and b) in any consistent units. The calculator will compute the hypotenuse (c) in the same units. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator find a or b if I know c and the other side?
A: This version calculates the hypotenuse (c) from the two legs. For finding a leg when you know the hypotenuse and other leg, you would rearrange the formula to \( a = \sqrt{c^2 - b^2} \).

Q2: Does this work for non-right triangles?
A: No, the Pythagorean Theorem only applies to right-angled triangles. For other triangles, you would use the Law of Cosines or Law of Sines.

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

Q4: How accurate are the results?
A: The calculator provides results accurate to two decimal places, though exact results may be irrational numbers for many inputs.

Q5: Can I use this for 3D space calculations?
A: The basic Pythagorean Theorem applies to 2D right triangles. For 3D space, you would need to extend it (e.g., \( d = \sqrt{a^2 + b^2 + c^2} \) for the space diagonal of a rectangular prism).