a² + b² = c²
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Pythagorean theorem calculator

Pythagorean theorem calculator will determine the length of the hypotenuse of a right triangle given the lengths of the two legs. It can also calculate the length of a missing leg given the lengths of the other leg and hypotenuse.  Finally, the area and perimeter are determined.

A right triangle is a triangle with an angle measuring 90 degrees. The hypotenuse is the leg opposite the 90 degree angle and the legs are the other two sides. Note that the other two angles must add to 90 degrees as well, since the sum of the measures of the angles of a triangle is 180.

Before using the Pythagorean theorem calculator, one must know what it is and what it does. It shows a relationship between the three sides of a right triangle.  If the legs of a right triangle are labeled a and b with hypotenuse labeled c, then a² + b² = c².  The theorem states that the sum of the squared of the sides of a right triangle equals the square of the hypotenuse.  The formula holds true for any right triangle.

For historical purposes and general knowledge, it must be noted that although Pythagoras was credited to first prove the theorem, there is no evidence to substantiate this.

An example using the Pythagorean theorem:

Suppose we know a and b and need the hypotenuse c.

If a = 4 and b = 6, for instance, then 4^2 + 6^2 = c^2

16 + 36 = c^2

52 = c^2

c is approximately 7.21

Now let's examine a scenario where we know c and one of the legs and need the other leg.

If c = 10 and a = 5, then

5^2 + b^2 = 10^2

25 + b^2 = 100

b^2 = 75

b is approximately 8.66

Calculating the area of the triangle is not difficult after knowing the lengths of the two sides.

A= (1/2)base*height

In a right triangle, the base and the height are a and b.

A = (1/2)ab

Also quite simple is calculating the perimeter, which is the sum of all the edges. Therefore, the perimeter of a right triangle is  P = a + b + c.

Working the Pythagorean theorem manually is not extensively difficult, but can be a little time consuming. Try the Pythagorean theorem calculator for lightning fast results to work your problem or check the work you obtained manually.