# Pythagorean Theorem Calculator

This calculator is designed to calculate unknown side lengths in right triangles using the Pythagorean Theorem.

This calculator is designed to calculate unknown side lengths in right triangles using the Pythagorean Theorem. Just enter the lengths of two sides of the right triangle and the calculator will give you the length of the third side. You can use this tool to explore the basic geometric relationships of right triangles and solve geometry problems.

When using the online Pythagorean Theorem calculator: by entering 1. edge and 2. edge you can calculate side a, side b or hypotenuse c.

Table of contents:

## How to Calculate the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the right sides is equal to the square of the hypotenuse. So, in a right triangle, with A and B being the right sides and C being the hypotenuse, the theorem is expressed as follows:

C^2 = A^2 + B^2Here:

**c:**represents the length of the hypotenuse (the longest side of a right triangle).**a and b:**represent the lengths of the right sides.

**Step-by-Step Calculation:**

- Determine the Right Sides: First, determine the right sides (A and B) of the right triangle.
- Square the Edges: Square the perpendicular sides A and B (A² and B²).
- Add them together: Find the sum of the squares (A² + B²).
- Take the Square Root: Take the square root to find the length of the hypotenuse from the result (C = √(A² + B²)).

### What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical theorem that expresses a fundamental relationship in right triangles. Named after the ancient Greek mathematician Pythagoras, it states that the sum of the squares of the right sides of a right triangle is equal to the square of the hypotenuse. So, if an angle of a triangle is 90 degrees, you can calculate the length of the hypotenuse by knowing the lengths of the other two sides.

This theorem is widely used in geometry, engineering, physics and many other fields, as well as in practical math problems. It is especially useful for calculating the hypotenuse of a triangle without knowing the lengths of its sides or, conversely, for finding perpendicular sides by knowing the length of the hypotenuse.

The Pythagorean Theorem is one of the fundamental mathematical relations and has played an important role in many mathematical discoveries and problem-solving processes. It also finds application in many areas of practical life.

**Mathematical Expression**

This expression allows us to find the length of the hypotenuse by taking the square root of the sum of the squares of the lengths of the perpendicular sides.

**History and Importance:**

The Pythagorean Theorem was discovered by Pythagoras, who lived in the 6th century BC. However, some sources suggest that this theorem was known even before Pythagoras. Ancient Babylonian and Indian mathematicians also used similar relations.

### Pythagorean Theorem Formula

The Pythagorean Theorem is represented by a mathematical formula that states that the sum of the squares of the perpendicular sides in a right triangle is equal to the square of the hypotenuse. This formula is used to analyze the geometry of right triangles and calculate unknown lengths.

Formula

C^2 = A^2 + B^2The Pythagorean Theorem is expressed as above.

Here:

**C:** hypotenuse (the longest side in a right triangle)

**A and 𝐵:** represent the right sides.

This formula is used to find the length of the hypotenuse “C” when you take the lengths of the right sides of a right triangle as “𝐴 and B”. It states that the sum of the squares of the right sides is equal to the square of the hypotenuse.

**Calculation Example:**

Consider a right triangle with perpendicular sides of 3 units and 4 units:

**A**= 3 units**B**= 4 units

In this case, we can find the length of the hypotenuse using the formula

C² = A² + B²

C² = 3² + 4²

C² = 9 + 16

C = √25

C = 5

With this calculation we find that the hypotenuse of a triangle with right sides of 3 units and 4 units is 5 units.

The Pythagorean Theorem Formula is an important tool for analyzing the geometric properties of right triangles and using it in practical problems.

### Uses of Pythagorean Theorem Calculation

The Pythagorean Theorem is a widely used mathematical tool for analyzing the geometric properties of right triangles and calculating unknown lengths. This theorem is used in practical applications in various fields and plays an important role in solving many problems.

**Construction and Engineering:**During the design and construction of buildings, it is very important to determine right angles and geometric relationships. The Pythagorean Theorem is often used to calculate geometric properties of buildings, bridges, roads and other structures. For example, the Pythagorean Theorem can be applied to check right angles in a structure or to determine the basic lengths in a bridge project.**Astronomy and Geography:**Measuring distances and performing geometric calculations is one of the main fields of astronomy and geography. The Pythagorean Theorem is used to calculate the distances of objects in the sky and to determine the distances between points on Earth.**Graphic Design and Computer Science:**Computer programs and graphic design software use the Pythagorean Theorem to create and manipulate geometric shapes. For example, in three-dimensional modeling software, the dimensions and angles of objects can be calculated using the Pythagorean Theorem.**Natural Sciences and Physics:**In physics, the Pythagorean Theorem can be used to analyze motion and calculate forces. For example, the properties of right-angled triangles can be used to calculate the speed or acceleration of an object.**Education and Training:**The Pythagorean Theorem is one of the cornerstones of mathematics education and plays an important role in geometry courses. Students learn to understand and apply geometric concepts by solving practical problems with this theorem.

These various uses of the Pythagorean Theorem help develop mathematical thinking and problem solving skills and provide many benefits in practical life.

### Interesting Facts about the Pythagorean Theorem

Pythagoras, the Ancient Greek Mathematician: The Pythagorean Theorem is named after Pythagoras, an ancient Greek mathematician and philosopher. However, whether the theorem belongs to Pythagoras is controversial. According to some historians, similar relationships were known before Pythagoras.

**Discovery of Geometric Relations:** The Pythagorean Theorem describes the geometric relationship between the sides of right triangles. This relationship is a fundamental tool for understanding the geometry of right triangles and for solving applied mathematics problems.

**Pythagorean Triangles:** Triangles that satisfy the Pythagorean Theorem are called “Pythagorean triangles”. In these triangles, the lengths of the perpendicular sides can be integers and the length of the hypotenuse is also an integer. The smallest Pythagorean triangle is the 3-4-5 triangle.

**Application Areas:** The Pythagorean Theorem is used in many fields such as engineering, architecture, astronomy, physics, graphic design and computer science. It plays an important role in various applications such as the design of structures, measurement of distances, geometric modeling and problem solving.

**Symbolic Representation:** The Pythagorean Theorem is represented by a simple mathematical formula that symbolically expresses the relationship between the sides of right triangles. This formula is used to analyze the geometric properties of right triangles and to calculate unknown lengths.

**Mathematical Thinking:** Understanding the Pythagorean Theorem helps develop mathematical thinking and problem solving skills. This theorem offers students the opportunity to learn to understand and apply geometric concepts.

These interesting facts of the Pythagorean Theorem help us understand the history of mathematics and its practical applications in our daily lives.