Question 1

What is the Pythagorean theorem?

Accepted Answer

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side, opposite the 90° angle) equals the sum of the squares of the other two sides: a² + b² = c². It is one of the most fundamental theorems in geometry.

Question 2

How do I calculate the hypotenuse?

Accepted Answer

If you know both legs (a and b), the hypotenuse c = √(a² + b²). For example, legs 3 and 4: c = √(9 + 16) = √25 = 5. Enter the two legs in the calculator and it computes the hypotenuse with full step-by-step working.

Question 3

How do I find a missing leg of a right triangle?

Accepted Answer

Rearrange the formula: b = √(c² − a²). For example, hypotenuse c = 13, leg a = 5: b = √(169 − 25) = √144 = 12. Enter the hypotenuse and the known leg to find the missing leg.

Question 4

What are Pythagorean triples?

Accepted Answer

Pythagorean triples are sets of three positive integers satisfying a² + b² = c². Common triples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25). Any integer multiple of a triple is also a triple — (6, 8, 10) is 2×(3, 4, 5). These appear frequently in homework problems and construction.

Question 5

Where is the Pythagorean theorem used in practice?

Accepted Answer

Construction (verifying right angles with the 3-4-5 rule: if the sides measure 3, 4, and 5 units, the corner is square), navigation (straight-line distance from coordinate differences), screen diagonal calculations (a 16×9 screen has diagonal √(16²+9²) = √337 ≈ 18.4 units), and physics (vector resultant magnitude).

Question 6

Is my data safe here?

Accepted Answer

Yes. Calculation runs in your browser. Nothing is sent to a server.

Pythagorean Theorem

Pythagorean theorem calculator

Pythagorean Theorem

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Pythagorean theorem calculator