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: \( a^2 + b^2 = c^2 \) where c is the hypotenuse.

2. How Does the Calculator Work?

The calculator uses the rearranged formula:

Where:

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

Note: The hypotenuse must be longer than the other known side.

3. Practical Applications

Construction: Calculating roof pitches, stair angles, or diagonal measurements.

Navigation: Determining shortest distances between points.

Engineering: Designing components with right-angle connections.

4. Using the Calculator

Steps:

1. Enter the length of known side (b)
2. Enter the length of hypotenuse (c)
3. Click Calculate to find the missing side (a)

5. Frequently Asked Questions (FAQ)

Q1: What if I know sides a and b but need c?
A: Use \( c = \sqrt{a^2 + b^2} \). This calculator solves for a when b and c are known.

Q2: Why does c have to be larger than b?
A: In a right triangle, the hypotenuse is always the longest side.

Q3: Can I use this for non-right triangles?
A: No, you would need the Law of Cosines for other triangles.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit will work.

Q5: How accurate are the results?
A: Results are mathematically precise based on your inputs.