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 fundamental relation in Euclidean geometry is used to calculate the length of any side of a right triangle when the lengths of the other two sides are known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Hypotenuse (meters)
• \( a \) and \( b \) — Other two sides (meters)

Explanation: Enter any two known sides to calculate the third unknown side. The calculator automatically determines which side to compute.

3. Importance of the Pythagorean Theorem

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

4. Using the Calculator

Tips:

• Enter any two known side lengths
• Leave the field you want to calculate empty
• All values must be positive numbers
• The hypotenuse must be longer than either side

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for non-right triangles?
A: No, this calculator only works for right-angled (90 degree) triangles. For other triangles, use the Law of Cosines.

Q2: What units should I use?
A: The calculator works with any consistent units (meters, feet, etc.), but results will be in the same unit as your inputs.

Q3: Why does it show an error when I enter three sides?
A: You should only enter two sides and leave the third field empty for calculation.

Q4: What if my hypotenuse is shorter than one side?
A: This violates the Pythagorean theorem - check your measurements as this cannot be a right triangle.

Q5: How accurate are the results?
A: Results are mathematically precise, but practical accuracy depends on your input measurements.