# Pythagorean Theorem Calculator

Explore right triangles and the Pythagorean Theorem with our calculator.

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## What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as:

a^{2} + b^{2} = c^{2}

Where:

- a and b are the lengths of the two legs of the right triangle
- c is the length of the hypotenuse

This equation is known as the Pythagorean equation, forming the basis of the Pythagorean Theorem. By knowing the lengths of two sides of a right triangle, we can use this theorem to calculate the length of the third side.

Pythagorean Theorem | c^{2} = a^{2} + b^{2} |

A median of a ( m_{a} ) | a × b / 2 |

Altitude of c (h) | a × b / c |

Angle Bisector of a | 2 × b × c × Cos(A/2) / (b + c) |

Angle Bisector of b | 2 × a × c × Cos(B/2) / (a + c) |

Angle Bisector of c (t_{c}) | t_{c}^{2} = 2 × a^{2} × b^{2} / (a + b)^{2} |

Median of a ( m_{a} ) | m_{a}^{2} = b^{2} + 0.25 × a^{2} |

Median of b ( m_{b} ) | m_{b}^{2} = a^{2} + 0.25 × b^{2} |

Median of c ( m_{c} ) | m_{c} = c / 2 |

Inscribed Circle Radius | a × b / ( a + b + c ) |

Circumscribed Circle Radius | c / 2 |

With the help of a Pythagorean Theorem Calculator, we can effortlessly determine the length of the third side by inputting the known values. This theorem finds applications in various fields, including architecture, navigation, electronics, and everyday problem-solving.