Pythagorean theorem calculator
The oldest useful theorem in mathematics, with both directions and the resulting angles.
Hypotenuse
5
- Other leg, given the hypotenuse and leg a
- 12.649 110 640 7
- Angle opposite leg a
- 36.869 90 degrees
- Angle opposite leg b
- 53.130 10 degrees
- Area of the triangle
- 6
- Perimeter
- 12
Show the working
- Leg a = 3
- Leg b = 4
- Hypotenuse (for the reverse) = 13
- Hypotenuse = hypot(3, 4) = 5
- Other leg, given the hypotenuse and leg a = 13 > 3 ? sqrt(13^2 - 3^2) : 0 = 12.6491
- Angle opposite leg a = 5 > 0 ? deg(asin(3 / 5)) : 0 = 36.8699
- Angle opposite leg b = 90 - 36.8699 = 53.1301
- Area of the triangle = 3 * 4 / 2 = 6
- Perimeter = 3 + 4 + 5 = 12
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- a^2 + b^2 = c^2
- missing leg = sqrt(c^2 - a^2)
3-4-5 and 5-12-13 are Pythagorean triples: all three sides come out as whole numbers.