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45-45-90 Triangle Calculator

Every side of an isosceles right triangle from one leg. The hypotenuse is always √2 times a leg, whatever the size.

With shortest side 6 ft, special right triangle comes to 8.4853 ft — hypotenuse. It is reached in 5 steps, the last of which is shortest * (kind_isosceles * sqrt(2) + kind_half_equilateral * 2), and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.

Formula and sources checked · How we check

Hypotenuse
8.4853 ft
Second side
shortest * (kind_isosceles + kind_half_equilateral * sqrt(3))6 ft
Hypotenuse
shortest * (kind_isosceles * sqrt(2) + kind_half_equilateral * 2)8.485 ft
Area
shortest * side_b / 218 sq ft
Perimeter
shortest + side_b + hypotenuse20.485 ft
Hypotenuse ÷ shortest side
hypotenuse / shortest1.414

The formula

  1. Second sideshortest * (kind_isosceles + kind_half_equilateral * sqrt(3))
  2. Hypotenuseshortest * (kind_isosceles * sqrt(2) + kind_half_equilateral * 2)
  3. Areashortest * side_b / 2
  4. Perimetershortest + side_b + hypotenuse
  5. Hypotenuse ÷ shortest sidehypotenuse / shortest

Formula from Wolfram MathWorld — special right triangles, NIST Digital Library of Mathematical Functions.

The same calculator, other cases

  • 30-60-90 Triangle CalculatorEvery side of a half-equilateral triangle from the shortest one. The hypotenuse is exactly twice it, and the third side √3 times it.

Undecided? The Special Right Triangle Calculator carries every case behind one control.

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