Pythagorean Theorem Calculator

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.

Check Pythagorean Theorem Worksheet.

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