1. What is the Pythagorean Theorem?

The Pythagorean Theorem states that 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. This fundamental relation is widely used in mathematics, physics, engineering and many practical applications.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

Where:

• \( a \) — Length of one side
• \( b \) — Length of other side
• \( c \) — Length of hypotenuse

Explanation: The theorem applies to all right-angled triangles, allowing calculation of any side when the other two are known.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are essential in construction, navigation, computer graphics, and many STEM fields. They form the basis for trigonometry and are used in calculating distances, angles, and vectors.

4. Using the Calculator

Tips: Enter lengths for sides a and b in any consistent units. Both values must be positive numbers. The calculator will compute the hypotenuse.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator find a or b if c is known?
A: This version calculates the hypotenuse (c) from sides a and b. For other calculations, rearrange the formula: \( a = \sqrt{c² - b²} \).

Q2: Does this work for non-right triangles?
A: No, the Pythagorean theorem only applies to right-angled triangles. For other triangles, use the Law of Cosines.

Q3: What units should I use?
A: Any consistent units can be used (cm, inches, meters, etc.), as long as both inputs are in the same units.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places, limited only by floating-point precision.

Q5: Can I calculate the area with this?
A: While this calculator focuses on side lengths, the area of a right triangle is simply \( \frac{1}{2} \times a \times b \).