1. What is the Hypotenuse Formula?

Definition: The hypotenuse formula calculates the longest side of a right-angled triangle using the Pythagorean theorem.

Purpose: It's essential in geometry, construction, navigation, and various engineering applications where right angles are involved.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The squares of the two shorter sides are added together, and the square root of this sum gives the hypotenuse length.

3. Importance of the Hypotenuse Calculation

Details: Accurate hypotenuse calculation ensures proper measurements in construction projects, roof framing, stair building, and any application involving right angles.

4. Using the Calculator

Tips: Enter the lengths of both sides (a and b) in meters. Both values must be > 0. The result will be in the same unit as the inputs.

5. Frequently Asked Questions (FAQ)

Q1: Can I use different units for the sides?
A: Yes, but both sides must use the same unit (both meters, both feet, etc.). The result will be in that same unit.

Q2: What if my triangle isn't right-angled?
A: This formula only works for right-angled triangles. For other triangles, you would need different formulas like the Law of Cosines.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise. Any inaccuracy would come from measurement errors in the input values.

Q4: Can I calculate a side if I know the hypotenuse and one side?
A: Yes, you can rearrange the formula: \( a = \sqrt{c^2 - b^2} \)

Q5: Why is this called the Pythagorean theorem?
A: It's named after the ancient Greek mathematician Pythagoras who first proved this relationship.