Pythagorean theorem calculator

Theorem in geometry is a proof - an argument establishing a property. A theorem is a statement that proves some property and requiring establishment. Theorems are also called lemmas, properties, consequences, rules, signs, affirmations.

Our Pythagorean theorem calculator makes it easy for you to calculate the length of the hypotenuse or either of the other two sides. Simply input the lengths of the two shorter sides of the right-angled triangle, and our calculator will automatically calculate the length of the hypotenuse or the missing side for you. This tool is perfect for students, engineers, architects, or anyone else who needs to make Pythagorean theorem calculations quickly and accurately.

What is Pythagorean theorem ?

The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right-angled triangle. The theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who first formulated it.

Pythagorean Theorem Formula

The Pythagorean theorem formula is:

c² = a² + b²

Where `a` and `b` are the lengths of the two shorter sides of the right-angled triangle, and `c` is the length of the hypotenuse.

Examples of Pythagorean Theorem

Example 1:

A right-angled triangle has a base of 6 cm and a height of 8 cm. What is the length of the hypotenuse?

Using the Pythagorean theorem formula: a² + b² = c²

We know that a = 6 cm and b = 8 cm, so:

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = √100 = 10

Therefore, the length of the hypotenuse is 10 cm.

Example 2:

A right-angled triangle has a hypotenuse of 10 cm and a base of 6 cm. What is the height of the triangle?

Using the Pythagorean theorem formula: a² + b² = c²

We know that c = 10 cm and a = 6 cm, so:

10² = 6² + b²

100 = 36 + b²

b² = 100 - 36

b = √64 = 8

Therefore, the height of the triangle is 8 cm.

Conclusion

In conclusion, the Pythagorean theorem is an essential concept in mathematics that describes the relationship between the sides of a right-angled triangle. Our Pythagorean theorem calculator can help you make calculations faster and more accurately. Whether you are a student, engineer, or architect, our calculator is the perfect tool to simplify your work.