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.

Purpose: This fundamental relation in Euclidean geometry is used to calculate distances and lengths in right-angled triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Hypotenuse (longest side)
• \( a \) — First side of the right angle
• \( b \) — Second side of the right angle

Explanation: The calculator takes the lengths of sides a and b, squares them, sums them, and then takes the square root to find the hypotenuse.

3. Importance of the Pythagorean Theorem

Details: This theorem is essential in construction, navigation, physics, computer graphics, and many other fields where distance calculations are needed.

4. Using the Calculator

Tips: Enter the lengths of the two perpendicular sides (a and b) in meters. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate a or b if I know c and the other side?
A: Yes! The formula can be rearranged as \( a = \sqrt{c² - b²} \) or \( b = \sqrt{c² - a²} \).

Q2: Does this only work for right-angled triangles?
A: Yes, the Pythagorean theorem applies exclusively to right-angled triangles.

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit can be used (cm, ft, etc.) as long as both sides use the same unit.

Q4: What if my triangle isn't right-angled?
A: You would need to use the Law of Cosines or other trigonometric formulas instead.

Q5: How accurate are the results?
A: The calculator provides results accurate to 3 decimal places.