Pythagorean Theorem Calculator with Degrees

What is the Pythagorean Theorem?

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right-angled triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It's widely used in various fields including construction, navigation, and engineering.

How to Use This Calculator

Using this calculator is simple. Follow these steps:

1. Enter the known side lengths of your right-angled triangle in the input fields.
2. If you know an angle, select which angle you're providing (α or β) and enter its value in degrees.
3. Click the "Calculate" button to compute the results.
4. Review the results, which will show the missing side lengths and angles.
5. Use the "Reset" button to clear all inputs and start over.

The calculator will automatically determine which values to calculate based on what information you provide.

Formula

The Pythagorean theorem is expressed as:

Where:

• c is the length of the hypotenuse
• a and b are the lengths of the other two sides

For angle calculations, we use trigonometric functions:

Where α and β are the angles opposite sides a and b, respectively.

Example Calculation

Let's solve a right-angled triangle with sides a = 3 units and b = 4 units.

1. Calculate the hypotenuse using the Pythagorean theorem:
   c = √(3² + 4²) = √(9 + 16) = √25 = 5 units
2. Calculate angle α:
   α = arctan(4/3) ≈ 53.13°
3. Calculate angle β:
   β = arctan(3/4) ≈ 36.87°

This confirms that the triangle is a classic 3-4-5 right-angled triangle.