Pythagorean Theorem Calculator

Calculate the length of a side in a right triangle

Enter the two sides of a right triangle to calculate the hypotenuse using the Pythagorean theorem (a² + b² = c²)

The Complete Guide to the Pythagorean Theorem

What is the Pythagorean Theorem?

The Pythagorean theorem is a fundamental principle in geometry, stating that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides:

a² + b² = c²

It is widely used in:

  • Calculating distances in geometry
  • Engineering and construction
  • Physics and trigonometry applications

Key Formulas for the Pythagorean Theorem

Calculating the Hypotenuse

c = √(a² + b²)

Use this formula to find the hypotenuse (c) when the lengths of both legs (a and b) are known.

Calculating a Missing Side

a = √(c² - b²)
b = √(c² - a²)

Rearrange the formula to calculate one of the legs if the hypotenuse and the other leg are known.

How to Use the Pythagorean Theorem Calculator: Step-by-Step

Step 1: Enter Known Sides

  • Input the lengths of two sides of a right triangle (a and b).
  • Ensure the values are positive and represent the triangle accurately.

Step 2: View the Hypotenuse

The calculator computes the hypotenuse (c) using the formula c = √(a² + b²) and displays the result.

Step 3: Solve for a Missing Side

If needed, enter the hypotenuse and one leg to calculate the missing side using rearranged formulas.

Practical Tips for Using the Pythagorean Theorem

Ensure Accuracy

  • Check that the triangle is a right triangle before applying the formula.
  • Use consistent units for all side lengths.

Real-World Applications

  • Use the theorem to calculate diagonal lengths in squares and rectangles.
  • Apply it in navigation and construction projects for accurate measurements.

Pythagorean Theorem FAQs

Can the Pythagorean theorem be used for all triangles?

No, the Pythagorean theorem applies only to right triangles. For non-right triangles, other methods like the Law of Cosines are needed.

How do I verify that a triangle is a right triangle?

Measure the sides and check if the equation a² + b² = c² holds true. If it does, the triangle is a right triangle.

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