1. What is the Hypotenuse?

The hypotenuse is the longest side of a right-angled triangle, opposite the right angle. It is calculated using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

• \( c \) — Hypotenuse (longest side)
• \( a \) — Length of one side
• \( b \) — Length of the other side

Explanation: The theorem applies to all right-angled triangles and is fundamental to geometry and trigonometry.

3. Importance of Hypotenuse Calculation

Details: Calculating the hypotenuse is essential in various fields including construction, navigation, physics, and engineering where right-angle measurements are required.

4. Using the Calculator

Tips: Enter the lengths of both sides (a and b) in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for any triangle?
A: No, this calculator specifically works for right-angled triangles only.

Q2: What units should I use for the measurements?
A: The calculator uses meters, but you can use any unit as long as both sides are measured in the same unit.

Q3: What if I know the hypotenuse and one side?
A: You can rearrange the formula to calculate the missing side: \( a = \sqrt{c^2 - b^2} \)

Q4: Does this work for 3D triangles?
A: The Pythagorean theorem can be extended to 3D: \( d = \sqrt{a^2 + b^2 + c^2} \)

Q5: What's the historical significance of this theorem?
A: The Pythagorean theorem is one of the most famous mathematical theorems, known since ancient times and attributed to the Greek mathematician Pythagoras.