# Pythagorean Theorem Calculator

Using the Pythagorean theorem, the Pythagorean Theorem Calculator determines the length of the third side of a right triangle depending on the lengths of the other two sides. The computations are quicker using The Mathematics Master online Pythagorean theorem calculator tool since it quickly displays the value of the unknown side.

$$a^2 + b^2 = c^2$$

## Pythagorean Theorem

The Pythagorean Theorem commonly referred to as Pythagoras’ Theorem, named after the Greek philosopher Pythagoras, is a fundamental relationship between a right triangle’s three sides. The Pythagorean theorem asserts that, given a right triangle, which is a triangle in which one of the angles is 90 degrees, the area of the square formed by the hypotenuse, the right triangle’s longest side, is equal to the sum of the areas of the squares formed by its other two sides:

## Pythagorean Theorem Formula

If you know the lengths of any two other sides, you can use the Pythagorean Theorem formula for right triangles to get the length of the third side. See the following formulas for solutions derived from the Pythagorean Theorem:

$$Perpendicular2 + Base^2 = Hypotenuse^2$$

(or)

$$a^2 + b^2 = c^2$$

$$a = \sqrt{c^2 – b^2}$$

$$b = \sqrt{c^2 – a^2}$$

$$c = \sqrt{a^2 + b^2}$$

## Example

Let a = 3 and b = 4

then we can determine the length of c as:

$$c = \sqrt{a^2 + b^2} = \sqrt{3^2+4^2} = \sqrt{25} = 5$$

We can calculate the length of any side of a triangle using the law of cosines which is a generalization of the Pythagorean theorem if we know the angles and lengths of the other two sides of the triangle. The law of cosines reduces to the Pythagorean equation if the angle between the opposite sides is a right angle.

## FAQs

What is the use of a special right triangle calculator?

Special right triangles have three defined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides using the special right triangle calculator. For example, the 45° – 45° – 90° triangle and the 30° – 60° – 90° triangle are other names for the two special right triangles.

What is the Pythagorean theorem calculator right triangle formula?

Pythagoras’ theorem asserts that: $$a^2 + b^2 = c^2$$ in a right triangle with cathetus a and b and with hypotenuse c. Take the square root of both sides to find the answer to the equation for c:

$$c = \sqrt{b^2 + a^2}$$. This Pythagorean theorem extension can be considered a “Hypotenuse Formula.”