1. What is the Pythagorean Theorem?

Definition: 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.

Formula: \( c^2 = a^2 + b^2 \) or rearranged to find a missing side: \( a = \sqrt{c^2 - b^2} \)

2. How Does the Calculator Work?

The calculator uses the rearranged Pythagorean theorem to find the missing side when you know:

• The hypotenuse (c)
• One other side (b)

It calculates the missing side (a) using the formula above.

3. Practical Applications

Construction: Calculating roof pitches, stair stringers, or ensuring square corners.

Navigation: Determining shortest distances between points.

Engineering: Designing components with right-angle relationships.

4. Using the Calculator

Tips:

• Enter the hypotenuse (longest side) as 'c'
• Enter the known side as 'b'
• Both values must be positive numbers
• The hypotenuse must be longer than the known side

5. Frequently Asked Questions (FAQ)

Q1: What if I know sides a and b but need c?
A: Use \( c = \sqrt{a^2 + b^2} \). We can create a different calculator for this case.

Q2: Why does the hypotenuse need to be longer?
A: By definition, the hypotenuse is always the longest side in a right triangle.

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit will work (cm, ft, etc.).

Q4: What if my result is imaginary?
A: This means your inputs don't form a valid right triangle (c ≤ b).

Q5: How accurate are the results?
A: Results are accurate to 3 decimal places for most practical applications.