Pythagorean Theorem | ScienceSim

a² + b² = c²

The Pythagorean Theorem

Drag the sliders to change side lengths and see how the areas adapt!

Side a (Vertical): 6

Side b (Horizontal): 8

3² + 4² = 5²

Our triangle has height a = 3 and base b = 4. Notice the squares built matching these lengths.

The red square has an area of 9 (3x3). The cyan square has an area of 16 (4x4).

Watch how all 9 + 16 blocks (25 total) perfectly fill the empty square on the hypotenuse c!

Live Calculation

Select a ratio to begin

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Understand the ratios by comparing side lengths of the right triangle.

Perpendicular (a): 6

Base (b): 8

Note: Trigonometry is fundamentally about the ratio of two sides, which stays constant regardless of the triangle size for a given angle.