Calculadora do teorema de Pitágoras

The Pythagorean theorem relates the three sides of a right triangle: a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle) and a and b are the two legs. Given any two sides, you can always solve for the third.

To solve for the hypotenuse, add the squares of the two legs and take the square root: c = √(a² + b²). To solve for a leg, rearrange to a = √(c² − b²) (or the equivalent for b) — this only works when c is longer than the known leg.

Example: a 3-4-5 triangle is a classic right triangle. With legs a = 3 and b = 4, the hypotenuse is c = √(3² + 4²) = √25 = 5. Enter any two of the three sides and leave the third at 0 to solve for it.

Pythagorean triples like 3-4-5, 5-12-13, and 8-15-17 appear often in construction squaring — multiples of triples work too (6-8-10).

Leave exactly one field at zero to solve for that side. Entering all three nonzero values checks whether they satisfy a² + b² = c² with c as hypotenuse.

Worked example with legs 3 and 4, hypotenuse left at 0: c = √(9+16) = 5. Swapping to find a leg with c=5 and b=4 gives a=3.

Distance formula in the coordinate plane is Pythagorean — distance from (0, 1) to (2, 5) uses legs Δx = 2, Δy = 4, hypotenuse √20 ≈ 4.47, the same relationship as checking whether a ladder reaches a wall safely on a construction site layout. Map scale drawings and roof sketches reuse the same right-triangle math with different unit labels.

Non-right triangles do not use a²+b²=c² — misapplying to 3-4-6 triangles gives wrong side; verify right angle before trusting output when all three sides are entered as check. 3-4-6 is not a right triangle — verify c is longest before checking a²+b²=c² when all three sides are entered nonzero.

Construction 3-4-5 squaring multiples to 6-8-10 for a 12-foot wall — measure 6 ft along one edge and 8 ft along perpendicular; diagonal must be 10 ft for square corners. 6-8-10 multiples square a twelve-foot wall — six and eight along legs, ten on diagonal confirms ninety-degree corners for framing.