# Pythagorean Theorem Calculator a: b: c:
Perimeter :
h (Height) :
Surface Area:
Angle α: °

Angle β: °

This Pythagorean Theorem Calculator will easily calculate angles, Perimeter, Height, Surface Area, sides or hypotenuse of triangles. Just enter the length of two sides.

## The Pythagorean theorem

The Pythagorean theorem is a theorem of Euclidean geometry which relates the lengths of the sides in a right triangle: the square of the length of the hypotenuse, which is the side opposite the right angle, is equal to the sum of squares of the lengths of the other two sides.

## Using the Pythagorean Theorem to calculate the length of one side of a right triangle

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If abc is a right triangle at a, then bc² = ab² + ac².

## Calculation of the length of the hypotenuse

bac is a right triangle at a, such that:

ba = 6.3 cm and ac = 8.4 cm.

Calculate bc.

In the triangle bac, rectangle at a, we apply the Pythagorean theorem.

bc² = ba² + ac²

bc² = 6.3² + 8.4²

bc² = 39.69 + 70.56

bc² = 110.25

bc = 110.25 = 10.5 cm

## Using the Pythagorean Theorem to prove that a triangle is right

If, in a triangle, the square of the longer side is equal to the sum of the squares of the other two sides, then that triangle is a right triangle.

If bc² = ab² + ac², then abc is rectangle in a.

Example

in the triangle bac: cb = 17 cm, ba = 10.2 cm and ca = 13.6 cm

What is the nature of the bac triangle?

cb² = 17² = 289

ba² + ca² = 10.2² + 13.6² = 104.04 + 184.96 = 289

cb² = ba² + ca²

So according to the reciprocal of the Pythagorean theorem, the tray triangle is right-angled in a.

## Using the Pythagorean Theorem to prove that a triangle is not right

If, in a triangle, the square of the longer side is not equal to the sum of the squares of the other two sides, then that triangle is not a right triangle.

If bc is the longest side and bc² ≠ ab² + ac², then abc is not a right triangle.

Example

in the triangle bac: cb = 3.2 cm, ba = 5.4 cm and ca = 4.3 cm

What is the nature of the bac triangle?

ba² = 5,4² = 29,16

cb² + ca² = 3,2² + 4,3² = 10,24 + 18,49= 28,73

cb² ≠ ba² + ca²

If bac were a right triangle, then by Pythagorean theorem we would have: cb² = ba² + ca², it is not, so bac is not a right triangle.