The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.

Pythagorean theorem online calculator

The calculator by means of the pythagorean function makes it possible to know if lengths satisfy the Pythagorean theorem. If the lengths contain variables, the calculator will seek to find the values of the variables which allow to verify the Pythagorean theorem.

The Pythagorean theorem is expressed as follows: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the opposite sides. If we consider the triangle ABC rectangle in A, if we put BC = a, AC = b, AB = c then the theorem of Pythagoras is written `BC^2=AB^2+AC^2` or `a^2=b^2+c^2`.

The Pythagorean theorem admits a reciprocal which states : If in a triangle the square of one side is equal to the sum of the squares of the opposite sides, then the triangle is a right triangle.

Verify that a triangle is a right triangle knowing the length of its sides

The calculator makes it possible to verify that a triangle is a right triangle knowing the length of the hypotenuse and the length of the opposite sides. If it is desired, for example, to verify that there exists a right-angled triangle whose hypotenuse has length 5 and the opposite sides for length 3 and 4, enter pythagorean(`3;4;5`). The calculator returns 1 if the values passed in parameter make it possible to deduce that the triangle is a right triangle, 0 otherwise. The calculator returns the details of the calculations used to use the Pythagorean theorem.

Find the length of one side of a right triangle from the length of the other two

The calculator allows you to find the length of one side knowing the two others thanks to the Pythagorean theorem. It is thus possible to calculate the length of the hypotenuse or the length of one of the sides adjacent to the right angle.

Find the length of the hypotenuse

The calculator allows to find the length of the hypotenuse if we know the length of the sides adjacent to the right angle. For example, if you are looking for the hypotenuse of a right-angled triangle whose adjacent sides are 3 and 4, you need to enter pythagorean(`3;4;x`), the value of the hypotenuse is then calculated.

Find the length of a side adjacent to the right angle

The calculator allows to find the length of a side adjacent to the right angle if we know the length of the hypotenuse and the length of the other adjacent side. For example, if you are looking for the length of the side of a right-angled triangle whose hypotenuse is 5 and the length of the other side is 3, you need to enter pythagorean(`x;3;5`), the value of the side adjacent to the right angle is then calculated.

It is also possible to find the length of the sides of an isosceles right triangle from the length of the hypotenuse. For example, if you are looking for the length of the sides adjacent to the right angle of an isosceles right triangle whose hypotenuse is 4, you must enter pythagorean(`x;x;4`).

Quiz on the Pythagorean theorem

In order to practice using the Pythagorean theorem, the site offers an application quiz.

Syntax :

pythagorean(length_adjacent_side;length_adjacent_side;hypotenuse_length)

Examples :

• pythagorean(`3;4;5`) returns 1
• pythagorean(`3;4;x`) returns 5