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 length of a missing leg when you know the hypotenuse and the other leg.

2. How Does the Calculator Work?

The calculator uses the rearranged Pythagorean theorem:

Where:

• \( a \) — The missing leg (length units)
• \( c \) — The hypotenuse (length units)
• \( b \) — The known leg (length units)

Explanation: The equation solves for the unknown leg by subtracting the square of the known leg 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, physics, engineering, architecture, and many practical applications like construction and navigation.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if my hypotenuse is shorter than the leg?
A: This is mathematically impossible in a right triangle. The hypotenuse is always the longest side. Check your measurements.

Q2: Can I use this for non-right triangles?
A: No, this calculator only works for right-angled triangles. For other triangles, you would need different formulas like the Law of Cosines.

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

Q4: How accurate are the results?
A: The results are mathematically exact (given perfect inputs). Rounding is done for display purposes only.

Q5: Can I calculate the hypotenuse with this?
A: No, this specific calculator finds a missing leg. A different calculator would be needed to find the hypotenuse.