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 calculator helps find the length of a missing side in a right triangle when you know the lengths of the other two sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of the missing side (units)
• \( b \) — Length of the known side (units)
• \( c \) — Length of the hypotenuse (units)

Explanation: The formula calculates the missing side by subtracting the square of the known side from the square of the hypotenuse, then taking the square root of the result.

3. Importance of Right Triangle Calculations

Details: These calculations are fundamental in geometry, construction, navigation, and various engineering applications where right angles are involved.

4. Using the Calculator

Tips: Enter the lengths of one side (b) and the hypotenuse (c). Both values must be positive numbers, and the hypotenuse must be longer than the side.

5. Frequently Asked Questions (FAQ)

Q1: What if I know sides a and b but not the hypotenuse?
A: Use the formula \( c = \sqrt{a^2 + b^2} \) to calculate the hypotenuse.

Q2: What units should I use?
A: Any consistent units (meters, feet, inches, etc.) can be used as long as all inputs are in the same unit.

Q3: Why does the hypotenuse need to be longer than the side?
A: In a right triangle, the hypotenuse is always the longest side, opposite the right angle.

Q4: What if I get an error?
A: Ensure the hypotenuse value is greater than the side value, and both are positive numbers.

Q5: Can this calculator work for non-right triangles?
A: No, this calculator only works for right-angled triangles. For other triangles, you would need to use the Law of Cosines or Law of Sines.