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 calculator helps find the missing side when you know the hypotenuse and one other side.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem rearranged to solve for the missing side:

Where:

• \( a \) — Missing side (length units)
• \( c \) — Hypotenuse (length units)
• \( b \) — Known side (length units)

Explanation: The equation calculates the length of the unknown 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: Right triangle calculations are fundamental in geometry, trigonometry, architecture, engineering, and many practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter the hypotenuse and known side lengths in any consistent units (meters, feet, etc.). The hypotenuse must be longer than the known side.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides but not the hypotenuse?
A: Use the standard form of the theorem: \( c = \sqrt{a^2 + b^2} \) where c is the hypotenuse.

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

Q3: What units should I use?
A: Any consistent length units can be used (meters, feet, inches, etc.), just ensure all measurements use the same units.

Q4: What if my hypotenuse is shorter than the other side?
A: This is impossible in a right triangle. The hypotenuse is always the longest side. Check your measurements.

Q5: How accurate are the results?
A: Results are as accurate as your input measurements. The calculator rounds to 2 decimal places.